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Constantes et fonctions mathématiques

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Compilation des constantes mathématiques, sélectionnées parmi les plus connues.

Ainsi comme les formules, les graphiques et les fractions continues qui leur sont associés.

Table de constantes et fonctions mathématiques[modifier | modifier le code]

Dans certaines formules le symbole ∞ est utilisé, si le calcul prend beaucoup de temps, peut être modifié à une valeur telle que 20 000, pour obtenir des résultats approximatifs.

Légende[modifier | modifier le code]

Valeur
Valeur numérique de la constante et lien MathWorld ou OEIS Wiki.
LaTeX
Formule ou série dans le format TeX.
Formule
Pour une utilisation dans Wolfram Alpha et faire des modifications.
OEIS
Encyclopédie en ligne des suites de nombres entiers.
Fraction continue
Dans la forme simple [partie entier ; frac1, frac2, frac3…], surligné si la fraction est périodique.
Année
Découverte de la constante, ou dates de l'auteur.
Format Web
Valeur de la constante, en format approprié pour les navigateurs Web.
Nº : Nombre
R - Rationnel
I - Irrationnel
A - Algébrique
T - Transcendant
C - Complexe

Table[modifier | modifier le code]

Valeur Nom Graphique Symbole LaTeX Formule OEIS Fraction continue Année Format Web
0,850 736 188 201 867 260 36[Mw 1] Constante du
pliage de papier
[1] ,[2]
Miura-ori.gif {P_f}  \sum_{n=0}^{\infty} \frac {8^{2^n}}{2^{2^{n+2}}-1} = 
\sum_{n=0}^{\infty} \cfrac {\tfrac {1}{2^{2^n}}} {1-\tfrac{1}{2^{2^{n+2}}}} N[Sum[n=0 to ∞]
{8^2^n/(2^2^
(n+2)-1)},37]
A143347 [0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6...] 0.85073618820186726036779776053206660
1,117 864 151 189 944 973 14[Mw 2] Constante de
Goh-Schmutz[3]
 C_{GS}  \int^\infty_0\frac{\log(s+1)}{e^{s}-1} \ ds =
\! - \! \sum_{n=1}^\infty \frac {e^n}{n} Ei(-n)
Ei = Exponentielle intégrale
Integrate{
log(s+1)
/(E^s-1)}
A143300 [1;8,2,15,2,7,2,1,1,1,1,2,3,5,3,5,1,1,4,13,1...] 1991 1.11786415118994497314040996202656544
6,580 885 991 017 920 970 85 Constante de Froda[4] ,[5]

2^{\,e} 2^e 2^e I ? [6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7...] 1963 6.58088599101792097085154240388648649
1,943 596 436 820 759 205 05[Mw 3] Indicatrice d'Euler[6],[7] EulerPhi100.PNG ET  \underset {p \text{= Premiers}}
{\prod_{p} \Big(1 + \frac{1}{p(p-1)}\Big)} = \frac {\zeta(2)\;\zeta(3)}{\zeta(6)}=\frac {315 \;\zeta(3)}{2\pi^4} zeta(2)*zeta(3)
/zeta(6)
A082695 [1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32...] 1750 1.94359643682075920505707036257476343
1,226 742 010 720 353 244 41[Mw 4] Constante Factorial de Fibonacci[8] F  \prod_{n = 1}^\infty \left(1 - \left( -\frac{1}{{\varphi}^2}\right)^n \right)=
\prod_{n = 1}^\infty \left(1 - \left( \frac{\sqrt{5}-3}{2}\right)^n \right) prod[n=1 to ∞]
{1-((sqrt(5) -3)/2)^n}
A062073 [1;4,2,2,3,2,15,9,1,2,1,2,15,7,6,21,3,5,1,23...] 1.22674201072035324441763023045536165
1,261 859 507 142 914 874 19[Mw 5] Dimension fractale du Flocon de Koch[9],[10] Von Koch curve.gif {C_k}  \frac{\log 4}{\log 3} log(4)/log(3) T A100831 [1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7...] 1.26185950714291487419905422868552171
1,772 453 850 905 516 027 29[Mw 6] Constante de Carlson-Levin[11]


{\Gamma}(\tfrac12) \sqrt{\pi} = \left(-\frac{1}{2}\right)! = \int_{-\infty }^{\infty } \frac {1}{e^{x^2}} \, dx  = \int_{0 }^{1} \frac {1}{\sqrt{-\ln x}} \, dx sqrt (pi) T A002161 [1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1...] 1.77245385090551602729816748334114518
2,029 883 212 819 307 250 04[Mw 7] Volume hyperbolique du complémentaire du Figure nœud de huit (en)[12] Blue Figure-Eight Knot.png {V_{8}}  2 \sqrt{3}\, \sum_{n=1}^\infty \frac{1}{n
{2n \choose n}} \sum_{k=n}^{2n-1} \frac{1}{k} = 
6 \int \limits_{0}^{\pi / 3} 
\log \left( \frac{1}{2 \sin t} \right) \, dt =

\scriptstyle
\frac{\sqrt{3}}{{9}}\, \sum \limits_{n=0}^\infty 
\frac{(-1)^n}{27^n}\,\left\{\!
\frac{{18}}{(6n+1)^2} - \frac{{18}}{(6n+2)^2} -
\frac{{24}}{(6n+3)^2} -
\frac{{6}}{(6n+4)^2} +
\frac{{2}}{(6n+5)^2}\!\right\}

6 integral[0 to pi/3]
{log(1/(2 sin (n)))}
A091518 [2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1...] 2.02988321281930725004240510854904057
0,286 747 428 434 478 734 10[Mw 8] Constante Strongly Carefree[13] K_{2}  \prod_{n=1}^\infty \underset{p_{n}: \, {premier}} {\left( 1-\frac{3 p_n-2}{{p_n}^{3}}\right)} = \frac {6}{\pi ^2}\prod_{n=1}^\infty \underset{p_{n}: \, {premier}} {\left( 1-\frac{1}{{p_n(p_n+1)}}\right)} N[ prod[k=1 to ∞]
{1 - (3*prime(k)-2)
/(prime(k)^3)}]
A065473 [0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7...] 0.28674742843447873410789271278983845
-4,227 453 533 376 265 408[Mw 9] Digamma (¼)[14] Complex Polygamma 0.jpg \psi (\tfrac14)  -\gamma -\frac{\pi}{2} - 3\ln{2} = -\gamma+\sum_{n=0}^{\infty}\left(\frac{1}{n+1}-\frac{1}{n+\tfrac14}\right) -EulerGamma
-\pi/2 -3 log 2
A020777 -[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4...] -4,2274535333762654080895301460966835
0,235 711 131 719 232 931 37[Mw 10] Constante de Copeland-Erdős[15] {\mathcal{C}_{CE}} \sum _{n=1}^\infty \frac{p_n} {10^{n + \sum \limits_{k=1}^n \lfloor \log_{10}{p_k} \rfloor }} sum[n=1 to ∞]
{prime(n) /(n+(10^
sum[k=1 to n]{floor
(log_10 prime(k))}))}
I A033308 [0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3...] 0.23571113171923293137414347535961677
2,094 551 481 542 326 591 48[Mw 11] Constante de Wallis[16] Wallis's Constant.png  W  \sqrt[3]{\frac{45-\sqrt{1929}}{18}}+\sqrt[3]{\frac{45+\sqrt{1929}}{18}} (((45-sqrt(1929))
/18))^(1/3)+
(((45+sqrt(1929))
/18))^(1/3)
A A007493 [2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4...] 1616
à
1703
2.09455148154232659148238654057930296
0,607 927 101 854 026 628 66[Mw 12] Constante de Hafner-Sarnak-McCurley (2)[17] \frac{1}{\zeta(2)}  \frac{6}{\pi^2} {=} \prod_{n = 0}^\infty \underset{p_{n}: \, {premier}}{\left(1- \frac{1}{{p_n}^2}\right)}{=}\textstyle  \left(1{-}\frac{1}{2^2}\right)\left(1{-}\frac{1}{3^2}\right)\left(1{-}\frac{1}{5^2}\right)... Prod{n=1 to ∞}
(1-1/prime(n)^2)
T A059956 [0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1...] 0.60792710185402662866327677925836583
0,747 597 920 253 411 435 17[Mw 13] Constante Parking de Rényi (de)[18] Random car parking problem.svg ParallelParkingAnimation2.gif {m}  \int \limits_{0}^{\infty} e^ {\left(\! -2 \int \limits_{0}^{x} \frac {1-e^{-y}}{y} dy\right)}\! dx = {e^{-2 \gamma}} \int \limits_{0}^{\infty} \frac{e^{-2 \Gamma(0,n)}}{n^2} [e^(-2*Gamma)] * Int{n,0,∞}[ e^(- 2*Gamma(0,n)) /n^2] A050996 [0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43...] 1958 0.74759792025341143517873094383017817
0,207 879 576 350 761 908 54[Mw 14] i élevé à i[19]

 {i}^{i}  e^{-\frac{\pi}{2}} e^(-pi/2) T A049006 [0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10...] 1746 0.20787957635076190854695561983497877
0,340 537 329 550 999 142 82[Mw 15] Constante de Pólya Random Walk[20] Walk3d 0.png {p(3)}  1- \!\!\left({3\over(2\pi)^3}\int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} {dx\,dy\,dz\over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}

 = 1- 16\sqrt{\tfrac23}\;\pi^3 \left(\Gamma(\tfrac{1}{24})\Gamma(\tfrac{5}{24})\Gamma(\tfrac{7}{24})\Gamma(\tfrac{11}{24})\right)^{-1}

1-16*Sqrt[2/3]*Pi^3
/((Gamma[1/24]
*Gamma[5/24]
*Gamma[7/24]
*Gamma[11/24])
A086230 [0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3...] 0.34053732955099914282627318443290289
36,462 159 607 207 911 770 99 Pi élevé à pi[21]

\pi ^\pi \pi ^\pi pi^pi A073233 [36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2...] 36.4621596072079117709908260226921236
1,584 962 500 721 156 181 45[Mw 16] Dimension de Hausdorff du Triangle de Sierpiński[22] SierpinskiTriangle-ani-0-7.gif {\log_2 3} \frac {\log 3}{\log 2} = \frac{\sum_{n=0}^\infty \frac{1}{2^{2n+1}(2n+1)}}{\sum_{n=0}^\infty \frac{1}{3^{2n+1}(2n+1)}} = \frac{\frac{1}{2}+\frac{1}{24}+\frac{1}{160}+...}{\frac{1}{3}+\frac{1}{81}+\frac{1}{1215}+...} ( Sum[n=0 to ∞]
{1/(2^(2n+1)(2n+1))})/
( Sum[n=0 to ∞]
{1/(3^(2n+1)(2n+1))})
T A020857 [1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1...] 1.58496250072115618145373894394781651
0,110 001 000 000 000 000 000 001[Mw 17] Nombre de Liouville[23]


\text{£}_{Li}  \sum_{n=1}^\infty \frac{1}{10^{n!}} = \frac {1}{10^{1!}} + \frac{1}{10^{2!}} + \frac{1}{10^{3!}} + \frac{1}{10^{4!}}  + ... Sum[n=1 to ∞]
{10^(-n!)}
T A012245 [1;9,1,999,10,9999999999999,1,9,999,1,9] 0.11000100000000000000000100...
0,463 647 609 000 806 116 21 Série de Machin-Gregory[24] Arctangent.svg \arctan \frac {1}{2}  {\sum_{n=0}^\infty \frac{\!\!(-1)^n}{(2n{+}1)2^{2n+1}} = \frac {1}{2} - \! \frac{1}{3 \cdot 2^3} {+} \frac{1}{5 \cdot 2^5} - \! \frac{1}{7 \cdot 2^7} {+}{...}} Sum[n=0 to ∞]
{(-1)^n (1/2)
^(2n+1)/(2n+1)}
I A073000 [0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1...] 0.46364760900080611621425623146121440
1,273 239 544 735 162 686 15 Série de Ramanujan-Forsyth[25] \frac {4}{\pi}  \displaystyle \sum \limits_{n=0}^{\infty} \textstyle \left(\frac{(2n-3)!!}{(2n)!!}\right)^{2} = {1 \! + \! \left(\frac {1}{2} \right)^2 \! {+} \left(\frac {1}{2 \cdot 4} \right)^2 \! {+} \left(\frac {1 \cdot 3}{2 \cdot 4 \cdot 6} \right)^2  {+} ...} Sum[n=0 to ∞]
{[(2n-3)!!
/(2n)!!]^2}
I A088538 [1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10...] 1.27323954473516268615107010698011489
15,154 262 241 479 264 189 7[Mw 18] Constante exponentiel itérative[26] Exp-esc.png e^e  \sum_{n=0}^\infty \frac{e^n}{n!} = \lim_{n \to \infty} \left(\frac {1+n}{n} \right)^{n^{-n}(1+n)^{1+n}} Sum[n=0 to ∞]
{(e^n)/n!}
A073226 [15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7...] 15.1542622414792641897604302726299119
1,156 362 684 332 269 716 85[Ow 1] Constante de récurrence cubique[27]


{\sigma_3} \prod_{n=1}^\infty n^{{3}^{-n}} = \sqrt[3] {1 \sqrt[3] {2 \sqrt[3] {3 \sqrt[3] {4 \cdots}}}} = 1^{^\tfrac{1}{3}} 2^{^\tfrac{1}{9}} 3^{^\tfrac{1}{27}} 4^{^\tfrac{1}{81}} \; \cdots prod[n=1 to ∞]
{n ^(1/3)^n}
A123852 [1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33...] 1.15636268433226971685337032288736935
0,707 106 781 186 547 524 40

+0,707 106 781 186 547 524 iErreur de référence : Balise <ref> incorrecte ; les références sans contenu doivent avoir un nom.

Racine carrée de i[28] Imaginary2Root.svg  \sqrt{i}  \sqrt[4]{-1} = \frac{1+i}{\sqrt{2}} = e^ \frac{i\pi}{4} =
 \cos\left (\frac{\pi}{4} \right ) + i\sin\left ( \frac{\pi}{4} \right ) (1+i)/(sqrt 2) C, A A010503

A010503
[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..]
= [0;1,2...]
[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] i
= [0;1,2...] i
0.70710678118654752440084436210484903
+ 0.70710678118654752440084436210484 i
0,596 347 362 323 194 074 34[Mw 19] Constante d'Euler-Gompertz[29] {G} \int\limits_{0}^{\infty} \frac{e^{-n}}{1+n} dn {=} \int\limits_{0}^{1} \! \frac{1}{1{-}\ln n} dn =
 \textstyle {\frac 1 {1+\frac 1{1+\frac 1{1+\frac 2{1+\frac 2{1+\frac 3{1+\frac 3{1+4{/...}} }}}}}}} N[int[0 to ∞]
{(e^-n)/(1+n)}]
I A073003 [0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1...] 0.59634736232319407434107849936927937
0,955 316 618 124 509 278 16 Angle magique[30] Magic angle.png  {\theta_m}  \arctan \left(\sqrt{2}\right) = \arccos \left(\sqrt{\tfrac13}\right) \approx \textstyle {54,7356} ^{ \circ } arctan(sqrt(2)) T A195696 [0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3...] 0.95531661812450927816385710251575775
3,246 979 603 717 467 061 05[Mw 20] Constante Silver de Tutte–Beraha[31]  \varsigma  2+2 \cos  \frac {2\pi} 7 = \textstyle 2+\frac{2+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}{1+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}} 2+2 cos(2Pi/7) A A116425 [3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2...] 3.24697960371746706105000976800847962
0,604 599 788 078 072 616 86[Mw 21] Relation entre l'aire d'un triangle équilatéral et son cercle inscrit. Fano plane.svg  \frac{\pi}{3 \sqrt 3}  \sum_{n = 1}^\infty \frac{1}{n{2n \choose n}} =  1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{5} + \frac{1}{7} - \frac{1}{8} + \cdots
Série de Dirichlet
Sum[1/(n
Binomial[2 n, n])
, {n, 1, ∞}]
T A073010 [0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6...] 0.60459978807807261686469275254738524
0,318 309 886 183 790 671 53[Mw 22] Inverse de Pi, Ramanujan[32]


\frac{1}{\pi}  \frac{2\sqrt{2}}{9801} \sum^\infty_{n=0} \frac{(4n)!\,(1103+26390 \; n)}{(n!)^4 \, 396^{4n}} 2 sqrt(2)/9801
*Sum[n=0 to ∞]
{((4n)!/n!^4)*(1103+
26390n)/396^(4n)}
T A049541 [0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2...] 0.31830988618379067153776752674502872
1,059 463 094 359 295 264 56[Ow 2] Intervalle de
demi-ton dans le
échelle musicale[33],[34]
Rast scale.svg

YB0214 Clavier tempere.png

\sqrt[12]{2}  \scriptstyle 440\, Hz. \textstyle 2^\frac{1}{12} \, 2^\frac{2}{12} \, 2^\frac{3}{12} \, 2^\frac{4}{12} \, 2^\frac{5}{12} \, 2^\frac{6}{12} \, 2^\frac{7}{12} \, 2^\frac{8}{12} \, 2^\frac{9}{12} \, 2^\frac{10}{12} \, 2^\frac{11}{12} \, 2

 \scriptstyle {\color{white}...\color{black} Do_1\;\;  Do\#\;\,  Re\;\,  Re\#\;\,  Mi\;\;  Fa\;\;  Fa\#\;  Sol\;\,  Sol\#\, La\;\;  La\#\;\;  Si\;\,  Do_2}  \scriptstyle {\color{white}....\color{black}C_1\;\;\;\;  C\#\;\;\;\,  D\;\;\;  D\#\;\;\,  E\;\;\;\;\,  F\;\;\;\,  F\#\;\;\;  G\;\;\;\;  G\#\;\;\;  A\;\;\;\,  A\#\;\;\;\,  B\;\;\;  C_2}

2^(1/12) A A010774 [1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2...] 1.05946309435929526456182529494634170
0,367 879 441 171 442 321 59[Mw 23] Inverse de
Nombre e[35]



\frac{1}{e} \sum_{n = 0}^\infty \frac{(-1)^n}{n!} = \frac{1}{0!} - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} +\cdots sum[n=2 to ∞]
{(-1)^n/n!}
T A068985 [0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12...]
= [0;2,1,1,2p,1], p∈ℕ
1618 0.36787944117144232159552377016146086
5,244 115 108 584 239 620 92[Mw 24] Constante
2 Lemniscate[36]
Lemniscate of Bernoulli.gif
2\varpi \frac{[\Gamma(\tfrac14)]^2}{\sqrt{2 \pi}} = 
4\int^1_0 \frac{dx}{\sqrt{(1-x^2)(2-x^2)}} Gamma[ 1/4 ]^2
/Sqrt[ 2 Pi ]
A064853 [5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2...] 1718 5.24411510858423962092967917978223883
1,306 377 883 863 080 690 46[Mw 25] Constante de Mills[37] {\theta}  \lfloor \theta^{3^{n}} \rfloor = \scriptstyle \text{ Premier} Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8) A051021 [1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2...] 1947 1.30637788386308069046861449260260571
0,788 530 565 911 508 961 06[Mw 26] Constante de Lüroth[38]
Constante de Lüroth.svg
C_L \sum_{n = 2}^\infty \frac{\ln\left(\frac{n}{n-1}\right)}{n} Sum[n=2 to ∞]
log(n/(n-1))/n
A085361 [0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16...] 0.78853056591150896106027632216944432
1,705 211 140 105 367 764 28[Mw 27] Constante de Niven (en)[39]


{C} 1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right) 1+ Sum[n=2 to ∞]
{1-(1/Zeta(n))}
A033150 [1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1...] 1969 1.70521114010536776428855145343450816
0,632 120 558 828 557 678 40[Mw 28] Constante de temps[40] Seq1.png {\tau}   \lim_{n \to \infty} 1-\frac {!n}{n!}=\lim_{n \to \infty} P(n)= \int_{0}^{1}e^{-x}dx = 1-\frac{1}{e} =

 \sum \limits_{n=0}^{\infty} \frac{(-1)^{n}}{n!} =
\frac{1}{1!}-\frac{1}{2!}+\frac{1}{3!}-\frac{1}{4!}+\frac{1}{5!}-\frac{1}{6!}+\cdots

lim_(n to ∞) (1- !n/n!)
 !n=subfactorielle
T A068996 [0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1...]
= [0;1,1,1,2n], n∈ℕ
0.63212055882855767840447622983853913
23,103 447 909 420 541 616 0[Mw 29] Série de Kempner(0)[41] {K_0} 1{+}\frac12{+}\frac13{+}\cdots{+}\frac19{+}\frac1{11}{+}\cdots{+}\frac1{19}{+}\frac1{21}{+}\cdots{+}\,\text{etc.}

{+}\frac1{99}{+}\frac1{111}{+}\cdots{+}\frac1{119}{+}\frac1{121}{+}\cdots\;\;
\overset {\text{Dénominateurs}}
\underset{\text{sont exclus.}}
{\scriptstyle \text{contenant des zéros}}

1+1/2+1/3+1/4+1/5
+1/6+1/7+1/8+1/9
+1/11+1/12+1/13
+1/14+1/15+...
A082839 [23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1...] 23.1034479094205416160340540433255981
0,835 648 848 264 721 053 33 Constante de Baker (ja)[42] Baker constant.png \beta_3 \int^1_0 \frac{{\mathrm{d} t}}{1 + t^3}=\sum_{n = 0}^\infty \frac{(-1)^n}{3n+1}= \frac{1}{3}\left(\ln 2+\frac{\pi}{\sqrt{3}}\right) Sum[n=0 to ∞]
{((-1)^(n))/(3n+1)}
A113476 [0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3...] 0.83564884826472105333710345970011076
0,194 528 049 465 325 113 61[Mw 30] Constante Du Bois Reymond[43]


{C_2} \frac{e^2-7}{2} = \int_0^\infty \left|{\frac{d}{dt}\left(\frac{\sin t}{t}\right)^n}\right|\,dt-1 (e^2-7)/2 T A062546 [0;5,7,9,11,13,15,17,19,21,23,25,27,29,31...]
= [0;2p+3], p∈ℕ
0.19452804946532511361521373028750390
0,989 431 273 831 146 951 74[Mw 31] Constante de Lebesgue[44] Fourier synthesis.svg {C_1} \lim_{n\to\infty}\!\! \left(\!{L_n{-}\frac{4}{\pi^2}\ln(2n{+}1)}\!\!\right)\!{=}
\frac{4}{\pi^2}\!\left({\sum_{k=1}^\infty \!\frac{2\ln k}{4k^2{-}1}}
{-}\frac{\Gamma'(\tfrac12)}{\Gamma(\tfrac12)}\!\!\right) 4/pi^2*[(2
Sum[k=1 to ∞]
{ln(k)/(4*k^2-1)})
-poligamma(1/2)]
A243277 [0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5...] 0.98943127383114695174164880901886671
1,187 452 351 126 501 054 59[Mw 32] Constante de Foias α (en)[45] F_\alpha  x_{n+1} = \left( 1 + \frac{1}{x_n} \right)^n\text{ pour }\, n=1,2,3,\ldots

La constante de Foias est l'unique nombre réel tel que: Si x1 = α alors la séquence diverge vers ∞. Lorsque x1 = α,  \lim_{n\to\infty}\! \scriptstyle x_n \!\frac{\log n}n {=} 1

A085848 [1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2...] 2000 1.18745235112650105459548015839651935
2,293 166 287 411 861 031 50[Mw 32] Constante de Foias β (en) Foias constant.png F_\beta  x^{n+1} = (x+1)^x x^(x+1)=(x+1)^x A085846 [2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1...] 2000 2.29316628741186103150802829125080586
1,745 405 662 407 346 863 49[Mw 33] Constante de Khintchine,
Moyenne harmonique[46]
Plot harmonic mean.png {K_{-1}}  \frac {\log 2} {\sum \limits_{n=1}^\infty \frac {1}{n}
 \log\bigl(1+\frac{1}{n(n+2)}\bigr)} = \lim_{n \to \infty} \frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}}

a1...an sont des éléments d'un fraction continue [a0;a1,a2...,an]

(log 2)/
(sum[n=1 to ∞]
{1/n log(1+
1/(n(n+2))}
A087491 [1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1...] 1.74540566240734686349459630968366106
0,108 410 151 223 111 361 51[Mw 34] Constante de Trott[47]  \mathrm{T}_1  \textstyle [1, 0, 8, 4, 1, 0, 1, 5, 1, 2, 2, 3, 1, 1, 1, 3, 6,...]

 \frac 1{1+\frac 1{0+\frac 1{8+\frac 1{4+\frac 1{1+\frac 1{0+1{/...}}}}}}}

Trott Constant A039662 [0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2...] 0.10841015122311136151129081140641509
1,851 937 051 982 466 170 36[Mw 35] Constante de Gibbs[48] Int si(x).PNG {\operatorname{Si}(\pi)}
Sinus
intégral
 \int_0^{\pi} \frac {\sin t}{t}\, dt =
\sum \limits_{n=1}^\infty (-1)^{n-1} \frac{\pi^{2n-1}}{(2n-1)(2n-1)!}

 =  \pi- \frac{\pi^3}{3*3!} + \frac{\pi^5}{5*5!} - \frac{\pi^7}{7*7!} + ...

SinIntegral[Pi] A036792 [1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39...] 1.85193705198246617036105337015799136
1,782 213 978 191 369 111 77[Mw 36] Constante de Grothendieck[49]


{K_{R}}  \frac {\pi}{2 \log(1+\sqrt{2})} = \frac {\pi}{2 \operatorname{arsinh} 1} pi/(2 log(1+sqrt(2))) A088367 [1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3...] 1.78221397819136911177441345297254934
1,110 720 734 539 591 561 75[Mw 37] Ratio d'un carré et le cercle circonscrit[50] Circumscribed2.png \frac{\pi}{2\sqrt 2} \sum_{n = 1}^\infty \frac{(-1)^{\lfloor \frac{n-1}{2}\rfloor}}{2n+1} = \frac{1}{1} + \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \frac{1}{9} + \frac{1}{11} - ... Sum[n=1 to ∞]
{(-1)^(floor((n-1)/2))/(2n-1)}
T A093954 [1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3...] 1.11072073453959156175397024751517342
2,826 419 997 067 591 575 54[Mw 38] Constante de Murata[51] {C_m}  \prod_{n = 1}^\infty \underset{p_{n}: \, {premier}}{ \Big(1 + \frac{1}{(p_n-1)^2}\Big)} Prod[n=1 to ∞]
{1+1/(prime(n)
-1)^2}
T ? A065485 [2;1,4,1,3,5,2,2,2,4,3,2,1,3,2,1,1,1,8,2,2,28...] 2.82641999706759157554639174723695374
1,523 627 086 202 492 106 27[Mw 39] Dimension fractale de la frontière de la Courbe du dragon[52] Fractal dragon curve.jpg {C_d} {\frac{\log\left(\frac{1+\sqrt[3]{73-6\sqrt{87}}+\sqrt[3]{73+6\sqrt{87}}}{3}\right)}
{\log(2)}} (log((1+(73-6
sqrt(87))^1/3+ (73+6 sqrt(87))^1/3)
/3))/ log(2)))
T [1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1...] 1.52362708620249210627768393595421662
1,014 941 606 409 653 625 02[Mw 40] Constante de Gieseking (de)[53] {\pi \ln \beta} \frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)=

\textstyle \frac{3\sqrt{3}}{4} \left( 1 {-} \frac{1}{2^2} {+} \frac{1}{4^2}{-}\frac{1}{5^2}{+}\frac{1}{7^2} {\pm} ... \right) = \displaystyle
\!\int_0^{\frac{2\pi}{3}} \! \ln \!\left(2 \cos \tfrac t2 \right) {\mathrm d}t

sqrt(3)*3/4 *(1
-Sum[n=0 to ∞]
{1/((3n+2)^2)}
+Sum[n=1 to ∞]
{1/((3n+1)^2)})
A143298 [1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11...] 1912 1.01494160640965362502120255427452028
2,236 067 977 499 789 696 40[Mw 41] Racine carrée de cinq
Somme de Gauss[54]
Pinwheel 1.svg  \sqrt{5}  \scriptstyle  (n = 5) \displaystyle  \sum_{k=0}^{n-1} e^{\frac{2 k^2 \pi i}{n}} = 1 + e^\frac{2 \pi i} {5} + e^\frac{8 \pi i} {5} + e^\frac{18 \pi i} {5} + e^\frac{32 \pi i} {5} Sum[k=0 to 4]
{e^(2k^2 pi i/5)}
A A002163 [2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4...]
= [2;4...]
2.23606797749978969640917366873127624
1,648 721 270 700 128 146 84 Racine carrée du nombre e[55]


\sqrt {e} \sum_{n = 0}^\infty \frac{1}{2^n n!} = \sum_{n = 0}^\infty \frac{1}{(2n)!!} = \frac{1}{1}+\frac{1}{2}+\frac{1}{8}+\frac{1}{48}+\cdots sum[n=0 to ∞]
{1/(2^n n!)}
T A019774 [1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1...]
= [1;1,1,1,4p+1], p∈ℕ
1.64872127070012814684865078781416357
1,017 343 061 984 449 139 71[Mw 42] Zeta(6)[56] Zeta.png \zeta(6) \frac{\pi^6}{945} = \prod_{n=1}^\infty \underset{p_{n}: \, {premier}}\frac{1}{{1-p_n}^{-6}} = \frac{1}{1{-}2^{-6}}{\cdot}\frac{1}{1{-}3^{-6}}{\cdot}\frac{1}{1{-}5^{-6}} ...

\textstyle = \sum_{n=1}^\infty\frac{{1}}{n^6} = \frac{1}{1^6} + \frac{1}{2^6} + \frac{1}{3^6} + \frac{1}{4^6} + \frac{1}{5^6} + ...

Prod[n=1 to ∞]
{1/(1-prime(n)^-6)}
T A013664 [1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1...] 1.01734306198444913971451792979092052
0,438 282 936 727 032 111 62 ···

0,360 592 471 871 385 485 i[Mw 18]

Tétration infinie de i[57]  {}^\infty {i}  \lim_{n \to \infty}  {}^n i  =  \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n 
= \frac {2 \, i}{\pi} \; {W} \!\left(\! -\frac{\pi \, i}{2}\right)
W() = Fonction W de Lambert
i^i^i^i^i^... C A077589
A077590
[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...]
+ [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] i
1758 0.43828293672703211162697516355126482
+ 0.36059247187138548595294052690600 i
3,625 609 908 221 908 311 93[Mw 43] Gamma(1/4)[58] Gamma abs 3D.png \Gamma(\tfrac14)  4 \left(\frac{1}{4}\right)!  = (2 \pi)^{\frac{3}{4}} \prod_{k=1}^\infty \tanh \left( \frac{\pi k}{2} \right) 4(1/4)! T A068466 [3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1...] 1729 3.62560990822190831193068515586767200
0,373 955 813 619 202 288 05[Mw 44] Constante de Artin[59] {C}_{Artin} \prod_{n=1}^{\infty} \left(1-\frac{1}{p_n(p_n-1)}\right)\quad p_n \scriptstyle \text{ = premier} Prod[n=1 to ∞]
{1-1/(prime(n)
(prime(n)-1))}
A005596 [0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46...] 1999 0.37395581361920228805472805434641641
1,854 074 677 301 371 918 43[Mw 45] Constante de la Lemniscate de Gauss[60] Lemniscate Building.gif  L \text{/}\sqrt{2} \int\limits_0^\infty \frac{{\mathrm{d} x}}{\sqrt{1 + x^4}}
 = \frac {1}{4\sqrt{\pi}} \,\Gamma \left(\frac {1}{4}\right)^2
 = \frac{4 \left(\frac {1}{4}!\right)^2} {\sqrt{\pi}}
Γ() = Fonction Gamma
pi^(3/2)/(2 Gamma(3/4)^2) A093341 [1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1...] 1.85407467730137191843385034719526005
262 537 412 640 768 743
,999 999 999 999 250 073[Mw 46]
Constante de Hermite-Ramanujan[61] {R}  e^{\pi\sqrt{163}} e^(π sqrt(163)) T A060295 [262537412640768743;1,1333462407511,1,8,1,1,5...] 1859 262537412640768743.999999999999250073
0,761 594 155 955 764 888 11[Mw 47] Tangente hyperbolique de 1 Hyperbolic Tangent.svg \operatorname{tanh} \, 1 \frac{e-\frac{1}{e}}{e+\frac{1}{e}} = \frac{e^2-1}{e^2+1} (e-1/e)/(e+1/e) T A073744 [0;1,3,5,7,9,11,13,15,17,19,21,23,25,27...]
= [0;2p+1], p∈ℕ
0.76159415595576488811945828260479359
4,532 360 141 827 193 809 62 Constante de van der Pauw (en)  {\alpha} \frac{\pi}{ln(2)} = \frac{\sum_{n = 0}^\infty \frac{4(-1)^n}{2n+1}} {\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n}} = \frac{\frac{4}{1} {-} \frac{4}{3} {+} \frac{4}{5} {-} \frac{4}{7} {+} \frac{4}{9} - ...} {\frac{1}{1}{-}\frac{1}{2}{+}\frac{1}{3}{-}\frac{1}{4}{+}\frac{1}{5}-...} π/ln(2) A163973 [4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1...] 4.53236014182719380962768294571666681
1,570 796 326 794 896 619 23[Mw 48] Produit de Wallis[62] Wallis product-chart.png {\frac{\pi}{2}}  \prod_{n=1}^{\infty} \left(\frac{4n^2}{4n^2 - 1}\right) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots Prod[n=1 to ∞]
{(4n^2)/(4n^2-1)}
T A069196 [1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...] 1655 1.57079632679489661923132169163975144
1,732 454 714 600 633 473 58[Ow 3] Constante inverse d'Euler-Mascheroni \frac {1}{\gamma}  \left(\int_{0}^{1} -\log \left(\log \frac{1}{x}\right)\, dx\right)^{-1} = \sum_{n=1}^\infty (-1)^n (-1+\gamma)^n 1/Integrate_
(x=0 to 1)
{-log(log(1/x))}
A098907 [1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11...] 1.73245471460063347358302531586082968
1,561 552 812 808 830 274 91 Nombre carré triangulaire de 2[63] Números triangulares.png {R_2} \frac{\sqrt{17}-1}{2} = \,\scriptstyle \sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\cdots}}}}}} \,\, -1

 = \,\scriptstyle \sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\cdots}}}}}} \textstyle

(sqrt(17)-1)/2 A A222133 [1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1...]
[1;1,1,3]
1.56155281280883027491070492798703851
1,082 323 233 711 138 191 51[Mw 42] Constante Zeta(4)[64]


\zeta(4)  \frac{\pi^4}{90} = \sum_{n=1}^\infty\frac{{1}}{n^4} = \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \frac{1}{4^4} + \frac{1}{5^4} + ... Sum[n=1 to ∞]
{1/n^4}
T A013662 [1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7...] ? 1.08232323371113819151600369654116790
0,872 284 041 065 627 976 17[Mw 49] Cercle de Ford[65] Circumferències de Ford.svg  A_{CF}  
\sum_{q\ge 1} \sum_{ (p, q)=1 \atop 1 \le p < q }\pi \left( \frac{1}{2 q^2} \right)^2 
= \frac{\pi}{4} \frac{\zeta(3)}{\zeta(4)}
= \frac{45}{2} \frac{\zeta(3)}{\pi^3}
ς() = Fonction zêta
pi Zeta(3)
/(4 Zeta(4))
[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3...] 0.87228404106562797617519753217122587
0,834 626 841 674 073 186 28[Mw 50] Constante de Gauss[66] {G}  \underset{ agm:\; moyenne \; arithm\acute{e}tique-g\acute{e}om\acute{e}trique} {\frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{4 \sqrt{2} \,(\tfrac14 !)^2}{\pi ^{3/2}}} (4 sqrt(2)
((1/4)!)^2)
/pi^(3/2)
T A014549 [0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1...] 1799 0.83462684167407318628142973279904680
1,259 921 049 894 873 164 76[Mw 51] Constante Delian (it)
racine cubique de 2[67]
Riemann surface cube root.jpg \sqrt[3]{2} \sqrt[3]{2} 2^(1/3) A A002580 [1;3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3...] -430 1.25992104989487316476721060727822835
0,809 394 020 540 639 130 71[Mw 52] Constante d'Alladi-Grinstead[68] {\mathcal{A}_{AG}}  e^{-1+\sum \limits_{k=2}^\infty \sum \limits_{n=1}^\infty \frac{1}{n k^{n+1}}} = e^{-1-\sum \limits_{k=2}^\infty \frac{1}{k} \ln \left( 1-\frac{1}{k}\right)} e^{(sum[k=2 to ∞]
|sum[n=1 to ∞]
{1/(n k^(n+1))})-1}
A085291 [0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22...] 1977 0.80939402054063913071793188059409131
0,007 874 996 997 812 384 4[Mw 53] Constante de Chaitin[69]
ProgramTree.svg
{\Omega}
\sum_{p \in P} 2^{-|p|} \overset {p: \; {Programme \; qui \; s'arr \hat ete}} \underset{ { \!\! P:\; Ensemble \; de \; tous \; les \; programmes \; qui \; s'arr \hat etent}}
{\scriptstyle {|p|}:\; Taille \; du \; programme }
Voir aussi: Problème de l'arrêt
T A100264 [0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1] 1975 0.0078749969978123844
1,131 988 248 794 3[Mw 54] Constante de Viswanath[70]


{C}_{Vi} \lim_{n \to \infty}|a_n|^\frac{1}{n} lim_(n→∞)
|F_n|^(1/n)
T ? A078416 [1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1...] 1997 1.1319882487943 ...
2,622 057 554 292 119 810 46[Mw 55] Constante de la Lemniscate (en)[71] Lemniscate of Gerono.svg {\varpi}  \pi \, {G} = 4 \sqrt{\tfrac2\pi}\,\Gamma{\left(\tfrac54 \right)^2} = \tfrac14 \sqrt{\tfrac{2}{\pi}}\,\Gamma {\left(\tfrac14 \right)^2} = 4 \sqrt{\tfrac2\pi}\left(\tfrac14 !\right)^2 4 sqrt(2/pi)
((1/4)!)^2
T A062539 [2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1...] 1798 2.62205755429211981046483958989111941
1,467 078 079 433 975 472 89[Mw 56] Constante de Porter[72] {C}  \frac{6\ln 2}{\pi ^2} \left(3 \ln 2 + 4 \,\gamma -\frac{24}{\pi ^2} \,\zeta '(2)-2 \right)-\frac{1}{2}

 \scriptstyle \gamma \, \text{= Constante de Euler–Mascheroni = 0,5772156649...}  \scriptstyle \zeta '(2) \,\text{= Dérivée de }\zeta(2) \,= \, - \!\!\sum \limits_{n = 2}^{\infty} \frac{\ln n}{n^2} \,\text{= −0,9375482543...}

6*ln2/Pi^2(3*ln2+ 4 EulerGamma- WeierstrassZeta'(2) *24/Pi^2-2)-1/2 A086237 [1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1...] 1975 1.46707807943397547289779848470722995
iErreur de référence : Balise <ref> incorrecte ; les références sans contenu doivent avoir un nom.
Unité imaginaire[73] Complex numbers imaginary unit.svg {i} \sqrt{-1} = \frac{\ln(-1)}{\pi} \qquad\qquad \mathrm{e}^{i\,\pi} = -1 sqrt(-1) CI 1501
à
1576
i
2,807 770 242 028 519 365 22[Mw 57] Constante de Fransén-Robinson[74]


{F} \int_{0}^\infty \frac{1}{\Gamma(x)}\, dx. = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, dx N[int[0 to ∞]
{1/Gamma(x)}]
A058655 [2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...] 1978 2.80777024202851936522150118655777293
0,123 456 789 101 112 131 41[Mw 58] Constante de Champernowne[75] Champernowne constant.svg C_{10} \sum_{n=1}^\infty\sum_{k=10^{n-1}}^{10^n-1}\frac{k}{10^{kn-9\sum_{j=0}^{n-1}10^j(n-j-1)}} T A033307 [0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15...] 1933 0.12345678910111213141516171819202123
0,624 329 988 543 550 870 99[Mw 59] Constante de Golomb-Dickman (en)[76] {\lambda} \int \limits_{0}^{\infty} \underset{Pour \; x>2}{\frac{f(x)}{x^2} dx} = \int \limits_{0}^{1} e^{Li(n)} dn \quad \scriptstyle \text{Li = Logarithmique intégrale} N[Int{n,0,1}[e^Li(n)],34] A084945 [0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1...] 1930
et
1964
0.62432998854355087099293638310083724
2,718 281 828 459 045 235 36[Mw 60] Nombre e, constante de Euler[77] Exp derivative at 0.svg {e} \sum_{n = 0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \cdots Sum[n=0 to ∞]
{1/n!}
T A001113 [2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1...]
= [2;1,2p,1], p∈ℕ
1618 2.71828182845904523536028747135266250
1,456 074 948 582 689 671 39[Mw 61] Constante de Backhouse (en)[78] {B} \lim_{k \to \infty}\left | \frac{q_{k+1}}{q_k} \right \vert  \quad \scriptstyle \text {où:} \displaystyle \;\; Q(x)=\frac{1}{P(x)}= \! \sum_{k=1}^\infty q_k x^k

 P(x) = \! \sum_{k=1}^\infty \underset{p_k: \, {Premier}}{p_k x^k} \!\! = 1{+}2x{+}3x^2{+}5x^3{+}7x^4{+}...

1/( FindRoot[0 == 1
+ Sum[x^n Prime[n],
{n, 10000}], {x, {1}})
A072508 [1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,4...] 1995 1.45607494858268967139959535111654355
2,584 981 759 579 253 217 06[Mw 62] Constante de Sierpiński[79] Random Sierpinski Triangle animation.gif  {K} \pi\left(2\gamma+\ln\frac{4\pi^3}{\Gamma(\tfrac{1}{4})^4}\right) =
  \pi (2 \gamma + 4 \ln\Gamma(\tfrac{3}{4}) - \ln\pi)

 = \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma (\tfrac{1}{4})\right)

-Pi Log[Pi]+2 Pi
EulerGamma
+4 Pi Log
[Gamma(3/4)]
A062089 [2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1...] 1907 2.58498175957925321706589358738317116
0,567 143 290 409 783 872 99[Mw 63] Constante Oméga, fonction W de Lambert[80] {\Omega}  \sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!} 
 =\,\left(\frac{1}{e}\right)
^{\left(\frac{1}{e}\right)
^{\cdot^{\cdot^{\left(\frac{1}{e}\right)}}}}
= e^{-\Omega} = {e}^{-e^{-e^{\cdot^{\cdot^{{-e}}}}}} Sum[n=1 to ∞]
{(-n)^(n-1)/n!}
T A030178 [0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1...] 1728
à
1777
0.56714329040978387299996866221035555
1,414 213 562 373 095 048 80[Mw 64] Racine carrée de deux, constante de Pythagore[81] Square root of 2 triangle.svg \sqrt{2} \prod_{n=1}^\infty 1+\frac{(-1)^{n+1}}{2n-1}
 = \left(1{+}\frac{1}{1}\right) \left(1{-}\frac{1}{3} \right)\left(1{+}\frac{1}{5} \right) \cdots prod[n=1 to ∞]
{1+(-1)^(n+1)
/(2n-1)}
A A002193 [1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2...]
= [1;2...]
< -800 1.41421356237309504880168872420969808
0,764 223 653 589 220 662 99[Mw 65] Constante de Landau-Ramanujan[82] K \frac1{\sqrt2}\prod_{p\equiv3\!\!\!\!\!\mod \! 4}\!\! \underset{\!\!\!\!\!\!\!\! p: \, {premier}}{\left(1-\frac1{p^2}\right)^{-\frac{1}{2}}}\!\!=\frac\pi4\prod_{p\equiv1\!\!\!\!\!\mod \!4}\!\! \underset{\!\!\!\! p: \, {premier}}{\left(1-\frac1{p^2}\right)^\frac{1}{2}} T ? A064533 [0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4...] 1908 0.76422365358922066299069873125009232
1,303 577 269 034 296 391 25[Mw 66] Constante de Conway[83] Conway constant.png {\lambda}  \begin{smallmatrix}
x^{71}\quad\ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\
-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\
+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\
-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\
-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad\ -7x^{21}+9x^{20}\\
+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\
+5x^{9}+x^{7}\quad\ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0 \quad\quad\quad
\end{smallmatrix} A A014715 [1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1...] 1987 1.30357726903429639125709911215255189
1,186 569 110 415 625 452 82[Mw 67] Constante de Khinchin-Lévy[84]


{\beta} \pi^2 / (12\,\ln 2) pi^2 /(12 ln 2) A100199 [1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9...] 1935 1.18656911041562545282172297594723712
1,451 369 234 883 381 050 28[Mw 68] Constante de Ramanujan-Soldner[85],[86] Integrallogrithm.png {\mu}  \mathrm{li}(x) = \int_0^x  \frac{dt}{\ln t} = 0 
\qquad \mathrm{li} \, \scriptstyle \text{= Logarithmique intégrale}

 \mathrm{li}(x)\;=\;\mathrm{Ei}(\ln{x}) \; \; 
\qquad \mathrm{Ei} \, \scriptstyle \text{= Exponentielle intégrale}

FindRoot[li(x) = 0] I A070769 [1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1...] 1792
à
1809
1.45136923488338105028396848589202744
0,353 236 371 854 995 984 54[Mw 69] Constante de Hafner-Sarnak-McCurley (en)[87] {\sigma}  \prod_{k=1}^{\infty}\left\{1-\left[1-\prod_{j=1}^n(1-p_k^{-j})\right]^2\right\} prod[k=1 to ∞]
{1-(1-prod[j=1 to n]
{1-prime(k)^-j})^2}
A085849 [0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3...] 1993 0.35323637185499598454351655043268201
0,636 619 772 367 581 343 07[Mw 70] 2/Pi, produit de Viète[88] Viète nested polygons.svg \frac{2}{\pi}  \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots 2/Pi T A060294 [0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4...] 1540
à
1603
0.63661977236758134307553505349005745
0,643 410 546 288 338 026 18[Mw 71] Constante de Cahen[89] \xi _{2}  \sum_{k=1}^{\infty} \frac{(-1)^{k}}{s_k-1} = \frac{1}{1} - \frac{1}{2} + \frac{1}{6} - \frac{1}{42} + \frac{1}{1806} {\,\pm \cdots}

sk sont des termes de la Suite de Sylvester 2, 3, 7, 43, 1807 ...
définie par  \, S_{0}= \, 2 , \,\, S_{k}= \, 1+\prod \limits_{n=0}^{k-1} S_{n} pour k>0

T A118227 [0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...] 1891 0.64341054628833802618225430775756476
1,381 356 444 518 497 793 37 Constante Beta Kneser-Mahler[90] \beta  e^{^{\textstyle{\frac{2}{\pi}} \displaystyle{\int_0^{\frac{\pi}{3}}} \textstyle{t \tan t\ dt}}} = 
         e^{^{\displaystyle{\,\int_{\frac{-1}{3}}^{\frac{1}{3}}} \textstyle{\,\ln \lfloor 1+e^{2 \pi i t}} \rfloor dt}} e^((PolyGamma(1,4/3)
- PolyGamma(1,2/3)
+9)/(4*sqrt(3)*Pi))
A242710 [1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1...] 1963 1.38135644451849779337146695685062412
0,662 743 419 349 181 580 97[Mw 72] Constante limite de Laplace[91] Laplace limit.png {\lambda}  \frac{ x \; e^\sqrt{x^2+1}}{\sqrt{x^2+1}+1} = 1 (x e^sqrt(x^2+1))
/(sqrt(x^2+1)+1)
= 1
A033259 [0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601...] 1782 ~ 0.66274341934918158097474209710925290
0,303 663 002 898 732 658 59[Mw 73] Constante de Gauss-Kuzmin-Wirsing[92] {\lambda}_{2} \lim_{n \to \infty}\frac{F_n(x) - \ln(1 - x)}{(-\lambda)^n} = \Psi(x),

\Psi(x) est une fonction analytique telle que \Psi(0) \!=\! \Psi(1) \!=\! 0.

A038517 [0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1...] 1974 0.30366300289873265859744812190155623
0,280 169 499 023 869 133 03[Mw 74] Constante de Bernstein (en)[93]


{\beta} \frac {1}{2\sqrt {\pi}} 1/(2 sqrt(pi)) T A073001 [0;3,1,1,3,9,6,3,1,3,14,34,2,1,1,60,2,2,1,1...] 1913 0.28016949902386913303643649123067200
0,577 215 664 901 532 860 60[Mw 75] Constante d'Euler-Mascheroni[94] Euler-Mas.jpg {\gamma}  \sum_{n=1}^\infty \sum_{k=0}^\infty \frac{(-1)^k}{2^n+k} 
\! = \!\sum_{n=1}^\infty \frac{1}{n} -\ln(n) \! = \!\! \int_{0}^{1}\!\! -\ln(\ln \frac{1}{x})\, dx sum[n=1 to ∞]
|sum[k=0 to ∞]
{((-1)^k)/(2^n+k)}
A001620 [0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1...] 1735 0.57721566490153286060651209008240243
0,661 707 182 267 176 235 15[Mw 76] Constante de Robbins[95] \Delta(3)  \frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5} (4+17*2^(1/2)-6
*3^(1/2)+21*ln(1+
2^(1/2))+42*ln(2+
3^(1/2))-7*Pi)/105
A073012 [0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1...] 1978 0.66170718226717623515583113324841358
1,435 991 124 176 917 432 35[Mw 31] Constante de Lebesgue[96],[97] Fourier series integral identities.gif {L_1}  \prod_{\begin{smallmatrix}i=0\\ j\neq i\end{smallmatrix}}^{n} \frac{x-x_i}{x_j-x_i} 
= \frac {1}{\pi} \int_0^{\pi} \frac {\lfloor \sin{\frac{3 t}{2}}\rfloor}{\sin{\frac{t}{2}}}\, dt = \frac {1}{3} + \frac {2 \sqrt{3}}{\pi} 1/3+2*sqrt(3)/Pi T A226654 [1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1...] 1902 ~ 1.43599112417691743235598632995927221
1,046 335 066 770 503 180 98 Constante mass Minkowski-Siegel[98]  F_1  \prod_{n=1}^{\infty} \frac{n!}{\sqrt{2\pi n}\left(\frac{n}{e}\right)^n \sqrt[12]{1+\tfrac1{n}}} N[prod[n=1 to ∞]
n! /(sqrt(2*Pi*n)
*(n/e)^n *(1+1/n)
^(1/12))]
A213080 [1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..] 1867
1885
1935
1.04633506677050318098095065697776037
1,860 025 079 221 190 307 18 Spirale de
Theodorus[99] ,[100]
Spiral of Theodorus.svg  \partial  \sum_{n=1}^{\infty} \frac{1}{\sqrt{n^3} + \sqrt{n}} =
\sum_{n=1}^{\infty} \frac{1}{\sqrt{n} (n+1)} Sum[n=1 to ∞]
{1/(n^(3/2)
+n^(1/2))}
A226317 [1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19...] -460
à
-399
1.86002507922119030718069591571714332
0,567 555 163 306 957 825 38[Mw 18] Module de tétration infini de i |{}^\infty {i} |  \lim_{n \to \infty} \left | {}^n i \right |  =\left | \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n  \right | Mod(i^i^i^...) A212479 [0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3...] 0.56755516330695782538461314419245334
0,261 497 212 847 642 783 75[Mw 77] Constante de Meissel-Mertens[101] Meissel–Mertens constant definition.svg {M} \lim_{n \rightarrow \infty } \!\! \left( 
\sum_{p \leq n} \frac{1}{p} \! - \ln(\ln(n))\! \right) 
\underset{\!\!\!\!  \gamma: \, \text{Constante de Euler} ,\,\, 
p: \, \text{premiers}}{\!\! = \! \gamma \! + \!\! \sum_{p} \!\left( \! 
\ln \! \left( \! 1 \! - \! \frac{1}{p} \! \right)
 \!\! + \! \frac{1}{p} \! \right)} gamma+
Sum[n=1 to ∞]
{\ln(1-1/prime(n))
+1/prime(n)}
T ? A077761 [0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296...] 1866
et
1873
0.26149721284764278375542683860869585
1,495 348 781 221 220 541 91 Racine quatrième de cinq[102] \sqrt[4]{5}  \sqrt[5]{5 \,\sqrt[5]{5 \, \sqrt[5]{5 \,\sqrt[5]{5 \,\sqrt[5]{5  \,\cdots}}}}} (5(5(5(5(5(5(5)
^1/5)^1/5)^1/5)
^1/5)^1/5)^1/5)
^1/5 ...
A A011003 [1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2...] 1.49534878122122054191189899414091339
4,669 201 609 102 990 671 85[Mw 78] Constante δ de Feigenbaum[103] LogisticMap BifurcationDiagram.png {\delta}  \lim_{n \to \infty}\frac {x_{n+1}-x_n}{x_{n+2}-x_{n+1}} \qquad \scriptstyle x \in (3,8284;\, 3,8495)

 \scriptstyle x_{n+1}=\,ax_n(1-x_n)\quad {o} \quad x_{n+1}=\,a\sin(x_n)

A006890 [4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5...] 1975 4.66920160910299067185320382046620161
2,502 907 875 095 892 822 28[Mw 78] Constante α de Feigenbaum[104]
Mandelbrot zoom.gif
\alpha \lim_{n \to \infty}\frac {d_n}{d_{n+1}} T ? A006891 [2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3...] 1979 2.50290787509589282228390287321821578
0,968 946 146 259 369 380 48 Beta(3)[105] {\beta} (3)  \frac{\pi^3}{32} = \sum_{n=1}^\infty\frac{-1^{n+1}}{(-1+2n)^3} = \frac{1}{1^3} {-} \frac{1}{3^3} {+} \frac{1}{5^3} {-} \frac{1}{7^3} {+} ... Sum[n=1 to ∞]
{(-1)^(n+1)
/(-1+2n)^3}
T A153071 [0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1...] 0.96894614625936938048363484584691860
1,902 160 583 104[Mw 79] Constante de Brun
= Σ inverses Nombres premiers jumeaux
[106]
Bruns-constant.svg {B}_{\,2}  \textstyle \underset{p,\, p+2: \, {premiers}}{\sum (\frac1{p}+\frac1{p+2})} = (\frac1{3} {+} \frac1{5}) + (\tfrac1{5} {+} \tfrac1{7}) + (\tfrac1{11} {+} \tfrac1{13}) + \dots N[prod[n=2 to ∞]
[1-1/(prime(n)
-1)^2]
A065421 [1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2] 1919 1.90216058310
0,870 588 379 9[Mw 79] Constante de Brun pour les quadruplets
= Σ inverses Nombres premiers jumeaux
[107]
{B}_{\,4} \underset{p,\, p+2,\, p+4,\, p+6: \, {premiers}}  {\left(\tfrac1{5} + \tfrac1{7} + \tfrac1{11} + \tfrac1{13}\right)}+ \left(\tfrac1{11} + \tfrac1{13} + \tfrac1{17} + \tfrac1{19}\right)+ \dots A213007 [0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1] 1919 0.87058837997
0,288 788 095 086 602 421 27[Mw 80] Flajolet and Richmond[108]


{Q}  \prod_{n=1}^{\infty} \left(1 - \frac{1}{2^n}\right) = \left(1{-}\frac{1}{2^1}\right) \left(1{-}\frac{1}{2^2} \right)\left(1{-}\frac{1}{2^3} \right) ... prod[n=1 to ∞]
{1-1/2^n}
A048651 [0;3,2,6,4,1,2,1,9,2,1,2,3,2,3,5,1,2,1,1,6,1...] 1992 0.28878809508660242127889972192923078
3,141 592 653 589 793 238 46[Mw 81] Nombre π, constante d'Archimède[109] ,[110] Sine cosine one period.svg  {\pi} \lim_{n\to \infty }\, 2^{n} \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\text{...} +\sqrt{2}}}}}_n Sum[n=0 to ∞]
{(-1)^n 4/(2n+1)}
T A000796 [3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2...] -250 ~ 3.14159265358979323846264338327950288
0,474 949 379 987 920 650 33[Mw 82] Constante de Weierstrass[111] \sigma(\tfrac12)  \frac{e^{\frac{\pi}{8}}\sqrt{\pi}}{4*2^{3/4} {(\frac {1}{4}!)^2}} (E^(Pi/8) Sqrt[Pi])/(4 2^(3/4) (1/4)!^2) A094692 [0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...] 1872 ? 0.47494937998792065033250463632798297
0,065 988 035 845 312 537 07[Mw 18] Limite inférieure de tétration[112] Infinite power tower.svg {e}^{-e} \left(\frac {1}{e}\right)^e 1/(e^e) A073230 [0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1...] 0.06598803584531253707679018759684642
1,282 427 129 100 622 636 87[Mw 83] Constante de Glaisher–Kinkelin (en)[113] {A}  e^{\frac{1}{12}-\zeta^{\prime}(-1)} = e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^{\infty} \frac{1}{n+1} \sum\limits_{k=0}^{n} \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)} e^(1/2-zeta´{-1}) T ? A074962 [1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35...] 1878 1.28242712910062263687534256886979172
0,783 430 510 712 134 407 05[Mw 84] Sophomore's dream (en)1
Jean Bernoulli[114]
Reve etudiant.svg {I}_{1} \int_0^1 \! x^x\,dx = \sum_{n = 1}^\infty \frac{(-1)^{n+1}}{n^n} = \frac{1}{1^1} - \frac{1}{2^2} + \frac{1}{3^3} - {\cdots} Sum[n=1 to ∞]
{-(-1)^n /n^n}
A083648 [0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14...] 1697 0.78343051071213440705926438652697546
1,291 285 997 062 663 540 40[Mw 84] Sophomore's dream (en)2
Jean Bernoulli[115]
Socd 001.png {I}_{2}  \int_0^1 \! \frac{1}{x^x}\, dx 
= \sum_{n = 1}^\infty \frac{1}{n^n} =  \frac{1}{1^1} + \frac{1}{2^2} + \frac{1}{3^3}  + \frac{1}{4^4}+ \cdots Sum[n=1 to ∞]
{1/(n^n)}
A073009 [1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4...] 1697 1.29128599706266354040728259059560054
0,660 161 815 846 869 573 92[Mw 85] Constante des Nombres premiers jumeaux[116] {C}_{2} \prod_{p=3}^\infty \frac{p(p-2)}{(p-1)^2} prod[p=3 to ∞]
{p(p-2)/(p-1)^2
A005597 [0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1...] 1922 0.66016181584686957392781211001455577
0,693 147 180 559 945 309 41[Mw 86] Logarithme naturel de 2 Alternating Harmonic Series.PNG \ln(2)  \sum_{n=1}^\infty \frac{1}{n 2^n} = 
\sum_{n=1}^\infty \frac{({-}1)^{n+1}}{n} 
= \frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+{\cdots} Sum[n=1 to ∞]
{(-1)^(n+1)/n}
T A002162 [0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10...] 1550
à
1617
0.69314718055994530941723212145817657
0,915 965 594 177 219 015 05[Mw 87] Constante de Catalan[117],[118] ,[119]


{\beta(2)}  \int_0^1 \!\! \int_0^1 \!\! \frac{1}{1{+}x^2 y^2}\, dx \,dy
= \! \sum_{n = 0}^\infty \! \frac{(-1)^n}{(2n{+}1)^2} \!
= \! \frac{1}{1^2}{-}\frac{1}{3^2}{+}{\cdots} Sum[n=0 to ∞]
{(-1)^n/(2n+1)^2}
T ? A006752 [0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11...] 1864 0.91596559417721901505460351493238411
0,785 398 163 397 448 309 61[Mw 88] Beta(1)[120] Loglogisticcdf.svg {\beta}(1) \frac{\pi}{4} = \sum_{n = 0}^\infty \frac{(-1)^n}{2n+1} = \frac{1}{1} - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \cdots Sum[n=0 to ∞]
{(-1)^n/(2n+1)}
T A003881 [0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5...] 1805
à
1859
0.78539816339744830961566084581987572
0,822 467 033 424 113 218 23[Mw 89] Constante Nielsen-Ramanujan[121]


\frac{{\zeta}(2)}{2}  \frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} {-} \frac{1}{2^2} {+} \frac{1}{3^2} {-} \frac{1}{4^2} {+} \frac{1}{5^2} {-} \cdots Sum[n=1 to ∞]
{((-1)^(n+1))/n^2}
T A072691 [0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...] 1909 0.82246703342411321823620758332301259
1,202 056 903 159 594 285 39[Mw 90] Constante d'Apéry[122] Apéry's constant.svg \zeta(3) \sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots=

\frac{1}{2} \sum_{n=1}^\infty \frac{H_n}{n^2} =
\frac{1}{2} \sum_{i=1}^\infty \sum_{j=1}^\infty \frac{1}{ij(i{+}j)}=
\!\!\int \limits_0^1 \!\!\int \limits_0^1 \!\!\int \limits_0^1 \frac{\mathrm{d}x \mathrm{d}y \mathrm{d}z}{1 - xyz}

Sum[n=1 to ∞]
{1/n^3}
I A002117 [1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11...] 1979 1.20205690315959428539973816151144999
1,233 700 550 136 169 827 35[Mw 91] Constante de Favard[123] \tfrac34\zeta(2)  \frac{\pi^2}{8} = \sum_{n = 0}^\infty \frac{1}{(2n-1)^2} = \frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots sum[n=1 to ∞]
{1/((2n-1)^2)}
T A111003 [1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1...] 1902
à
1965
1.23370055013616982735431137498451889
1,539 600 717 839 002 038 69[Mw 92] Constante Square Ice de Lieb (en)[124] Sixvertex2.png {W}_{2D} \lim_{n \to \infty}(f(n))^{n^{-2}}=\left(\frac{4}{3}\right)^\frac{3}{2} = \frac {8 \sqrt{3}} {9} (4/3)^(3/2) A A118273 [1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2...] 1967 1.53960071783900203869106341467188655
1,644 934 066 848 226 436 47[Mw 93] Zeta(2) {\zeta}(\,2)  \frac{\pi^2}{6} = \sum_{n=1}^\infty\frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots Sum[n=1 to ∞]
{1/n^2}
T A013661 [1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15...] 1826
à
1866
1.64493406684822643647241516664602519
1,444 667 861 009 766 133 65[Mw 94] Nombre de Steiner[125]
Infinite power tower.svg
\sqrt[e]{e} e^{1/e}
Limite supérieure de Tétration
e^(1/e) A073229 [1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9...] 1796
à
1863
1.44466786100976613365833910859643022
1,606 695 152 4152 917 637 8[Mw 95] Constante d'Erdős-Borwein[126] ,[127]


{E}_{\,B} \sum_{m=1}^{\infty} \sum_{n=1}^{\infty}\frac{1}{2^{mn}} =\sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} \! + \! \frac{1}{3} \! + \! \frac{1}{7} \! + \! \frac{1}{15} \! + \! ... sum[n=1 to ∞]
{1/(2^n-1)}
I A065442 [1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1...] 1949 1.60669515241529176378330152319092458
1,618 033 988 749 894 848 20[Mw 96] Phi,
Nombre d'or
Animation GoldenerSchnitt.gif {\varphi} \frac{1 + \sqrt{5}}{2} = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}} (1+5^(1/2))/2 A A001622 [0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1...]
= [0;1...]
-300 ~ 1.61803398874989484820458633436563812
2,665 144 142 690 225 188 65[Mw 97] Constante de Gelfond-Schneider[128]  G_{\,GS} 2^{\sqrt{2}} 2^sqrt{2} T A007507 [2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1...] 1906
à
1968
2.66514414269022518865029724987313985
1,732 050 807 568 877 293 52[Mw 98] Constante de Theodorus[129] Square root of 3 in cube.svg \sqrt{3}  \sqrt[3]{3 \,\sqrt[3]{3 \, \sqrt[3]{3 \,\sqrt[3]{3 \,\sqrt[3]{3  \,\cdots}}}}} (3(3(3(3(3(3(3)
^1/3)^1/3)^1/3)
^1/3)^1/3)^1/3)
^1/3 ...
A A002194 [1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2...]
= [1;1,2...]
-465
à
-398
1.73205080756887729352744634150587237
1,757 932 756 618 004 532 70[Mw 99] Nombre de Kasner {R} \sqrt{1 + \sqrt{2 + \sqrt{3 + \sqrt{4 + \cdots}}}} A072449 [1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2...] 1878
à
1955
1.75793275661800453270881963821813852
2,295 587 149 392 638 074 03[Mw 100] Constante parabolique universelle (en)[130] Qfunction.png  {P}_{\,2} \ln(1 + \sqrt2) + \sqrt2 ln(1+sqrt 2)+sqrt 2 T A103710 [2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8...] 2.29558714939263807403429804918949038
3,302 775 637 731 994 646 55[Mw 101] Nombre de bronze[131]


{\sigma}_{\,Rr} \frac {3+\sqrt{13}}{2} = 1+\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}} (3+sqrt 13)/2 A A098316 [3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3...]
= [3;3...]
3.30277563773199464655961063373524797
0,187 859 642 462 067 120 24[Mw 102] Constante de MRB (en), Marvin Ray Burns[132],[133],[134] MRB-Gif.gif  C_{{}_{MRB}}  \sum_{n=1}^{\infty} (\! - \! 1)^n (\sqrt[n]{n}\!-1) = \sum_{k=1}^{\infty} \left((2k)^{\frac{1}{2k}} - (2k-1)^{\frac{1}{2k-\!1}}\right) Sum[n=1 to ∞]
{(-1)^n (n^(1/n)-1)}
T ? A037077 [0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1...] 1999 0.18785964246206712024851793405427323
4,132 731 354 122 492 938 46 Racine de
2 e pi[135]
 \sqrt{2e \pi}  \sqrt{2e \pi} sqrt(2e pi) A019633 [4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4...] 4.13273135412249293846939188429985264
2,506 628 274 631 000 502 41 Racine carrée de
2 pi
Stirling's Approximation Small.png \sqrt{2 \pi} \lim_{n \to \infty} \frac {n! \; e^n}{n^n \sqrt{n}}
Formule de Stirling
sqrt (2*pi) T A019727 [2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3...] 1692
à
1770
2.50662827463100050241576528481104525
3,275 822 918 721 811 159 78[Mw 103] Constante de Khinchin-Lévy


\gamma \lim_{n \to \infty}{q_n}^{1/n}= e^{\pi^2/(12\ln2)} e^(\pi^2/(12 ln(2)) A086702 [3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55...] 1936 3.27582291872181115978768188245384386
23,140 692 632 779 269 005 7[Mw 104] Constante de Gelfond[136] {e}^{\pi}  (-1)^{-i} = i^{-2i} = \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2!} + \frac{\pi^{3}}{3!} + \cdots Sum[n=0 to ∞]
{(pi^n)/n!}
T A039661 [23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1...] 1906
à
1968
23.1406926327792690057290863679485474
3,359 885 666 243 177 553 17[Mw 105] Constante de Prévost[137] Somme inverses de Fibonacci  \Psi \sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} +  \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots Sum[n=1 to ∞] {1/F_n} I A079586 [3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362...] 1977 3.35988566624317755317201130291892717
1,324 717 957 244 746 025 96[Mw 106] Nombre plastique[138] Nombre plastique.svg {\rho} \sqrt[3]{1 + \! \sqrt[3]{1 + \! \sqrt[3]{1 + \cdots}}} = \textstyle \sqrt[3]{\frac{1}{2}+ \! \sqrt{\frac{23}{108}}}+ \! \sqrt[3]{\frac{1}{2}- \! \sqrt{\frac{23}{108}}} (1+(1+(1+(1+(1+(1
)^(1/3))^(1/3))^(1/3))
^(1/3))^(1/3))^(1/3)
A A060006 [1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8...] 1929 1.32471795724474602596090885447809734
2,373 138 220 831 250 905 64 Constante de Lévy2[139]


2\,\ln\,\gamma \frac{\pi^2}{6\ln(2)} Pi^(2)/(6*ln(2)) T A174606 [2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2...] 1936 2.37313822083125090564344595189447424
9,869 604 401 089 358 618 83 Pi élevé au carré {\pi} ^2 6 \sum_{n=1}^\infty \frac{1}{n^2} = \frac{6}{1^2} + \frac{6}{2^2} + \frac{6}{3^2} + \frac{6}{4^2}+ \cdots 6 Sum[n=1 to ∞]
{1/n^2}
T A002388 [9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5...]


9.86960440108935861883449099987615114
2,685 452 001 065 306 445 30[Mw 107] Constante de Khintchine[140] KhinchinBeispiele.svg  K_{\,0}  \prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\ln n/\ln 2} prod[n=1 to ∞]
{(1+1/(n(n+2)))
^((ln(n)/ln(2))}
T A002210 [2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2...] 1934 2.68545200106530644530971483548179569

Notes et références[modifier | modifier le code]

  1. Francisco J. Aragón Artacho, David H. Baileyy, Jonathan M. Borweinz, Peter B. Borwein, Tools for visualizing real numbers.,‎ (lire en ligne [PDF]), p. 33
  2. Jürgen Giesen, Papierfalten, Universität Duisburg-Essen,‎ (lire en ligne [PDF])
  3. Steven R. Finch, Mathematical Constants, Cambridge University Press,‎ (ISBN 3-540-67695-3, lire en ligne), p. 287
  4. Christoph Zurnieden, Descriptions of the Algorithms (lire en ligne)
  5. Simon Plouffe, The Froda constant (lire en ligne)
  6. Benjamin Klopsch, NOTE DI MATEMATICA: Representation growth and representation zeta functions of groups, Univ. del Salento,‎ (ISSN 1590–0932, lire en ligne [PDF]), p. 114
  7. Nikos Bagis, Some New Results on Prime Sums (3 The Euler Totient constant), Aristotle University of Thessaloniki (lire en ligne [PDF]), p. 8
  8. (en) Sergey Kitaev and Toufik Mansour, 2007, « The problem of the pawns », .
  9. Chan Wei Ting ..., Moire patterns + fractals (lire en ligne [PDF]), p. 16
  10. Coralie AYACHE, La dimension fractale du flocon de Niel von Koch, Université Paris Diderot,‎ (lire en ligne)
  11. H.M. Antia, Numerical Methods for Scientists and Engineers, Birkhäuser Verlag,‎ (ISBN 3-7643-6715-6, lire en ligne), p. 220
  12. Jonathan Borwein,David Bailey, Mathematics by Experiment: Plausible Reasoning in the 21st Century, A K Peters, Ltd.,‎ (ISBN 978-1-56881-442-1, lire en ligne), p. 56
  13. Steven R. Finch, Quadratic Dirichlet L-Series, Harvard University,‎ (lire en ligne [PDF]), p. 12
  14. Horst Alzera, Dimitri Karayannakisb, H.M. Srivastava, Series representations for some mathematical constants, Elsevier Inc,‎ (lire en ligne), p. 149
  15. Yann Bugeaud, Distribution Modulo One and Diophantine Approximation, Cambridge University Press,‎ (ISBN 978-0-521-11169-0, lire en ligne), p. 87
  16. David Eugene Smith, A Source Book in Mathematics, McGraw-Hill Book Company. Ihc,‎ (lire en ligne [PDF]), p. 250
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  19. Reinhold Remmert, Theory of Complex Functions, Springer,‎ (ISBN 0-387-97195-5, lire en ligne), p. 162
  20. Steven R. Finch, Mathematical Constants, Cambridge University Press,‎ (ISBN 978-0-521-81805-6, lire en ligne), p. 322
  21. Renzo Sprugnoli., Introduzione alla Matematica, Universita di Firenze (lire en ligne [PDF])
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  23. Calvin C. Clawson, Mathematical Traveler: Exploring the Grand History of Numbers, Perseus,‎ (ISBN 0-7382-0835-3, lire en ligne), p.187
  24. John Horton Conway, Richard K. Guy, The Book of Numbers, Copernicus,‎ (ISBN 0-387-97993-X, lire en ligne), p. 242
  25. Xavier Gourdon, Pascal Sebah., Collection of series for Pi (lire en ligne)
  26. R. A. Knoebel., Exponentials Reiterated, Maa.org (lire en ligne [PDF])
  27. J. Sondow., Generalization of Somos Quadratic (lire en ligne [PDF])
  28. Robert Kaplan,Ellen Kaplan, The Art of the Infinite: The Pleasures of Mathematics, Oxford University Press,‎ (ISBN 978-1-60819-869-6, lire en ligne), p. 238
  29. Annie Cuyt, Viadis Brevik Petersen, Brigitte Verdonk, William B. Jones, Handbook of continued fractions for special functions, Springer,‎ (ISBN 978-1-4020-6948-2, lire en ligne), p. 190
  30. Andras Bezdek, Discrete Geometry, Marcel Dekkcr, Inc.,‎ (ISBN 0-8247-0968-3, lire en ligne), p. 150
  31. D. R. Woodall, Chromatic Polynomials Of Plane Triangulations, University of Nottingham,‎ (lire en ligne [PDF]), p. 5
  32. J.L. Berggren, Jonathan M. Borwein, Peter Borwein, Pi: A Source Book, Springer-Verlag,‎ (ISBN 0-387-20571-3, lire en ligne), p. 637
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  35. Eli Maor, "e": The Story of a Number, Princeton University Press,‎ (ISBN 978-0-691-14134-3, lire en ligne), p. 37
  36. Evaluation of the complete elliptic integrals by the agm method (lire en ligne)
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  38. Steven Finch, Continued Fraction Transformation III, Harvard University,‎ (lire en ligne [PDF]), p. 5
  39. Ivan Niven, Averages of exponents in factoring integers (lire en ligne [PDF])
  40. Kunihiko Kaneko,Ichiro Tsuda, Complex Systems: Chaos and Beyond,‎ (ISBN 3-540-67202-8, lire en ligne), p. 211
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  44. Horst Alzer, Journal of Computational and Applied Mathematics, Volume 139, Issue 2, Elsevier,‎ , 215–230 p. (lire en ligne)
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  104. K. T. Chau,Zheng Wang, Chaos in Electric Drive Systems: Analysis, Control and Application, John Wiley & Son,‎ (ISBN 978-0-470-82633-1, lire en ligne), p. 7
  105. Michael A. Idowu, Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function, arXiv:1210.5559,‎ (lire en ligne), p. 1
  106. Thomas Koshy, Elementary Number Theory with Applications, Elsevier,‎ (ISBN 978-0-12-372-487-8, lire en ligne), p. 119
  107. Pascal Sebah and Xavier Gourdon, Introduction to twin primes and Brun’s constant computation,‎ (lire en ligne)
  108. Michael Jacobson,Hugh Williams, Solving the Pell Equation, Springer,‎ (ISBN 978-0-387-84922-5, lire en ligne), p. 159
  109. Michael Trott, The Mathematica GuideBook for Programming, Springer Science,‎ (ISBN 0-387-94282-3, lire en ligne), p. 173
  110. James T. Smith, Methods of Geometry, John Wiley & Sons,‎ (ISBN 0-471-25183-6, lire en ligne), p. 123
  111. Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, Second Edition, CRC Press,‎ (ISBN 1-58488-347-2, lire en ligne), p. 151
  112. Jonathan Sondowa, Diego Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae,‎ (lire en ligne [PDF])
  113. Jan Feliksiak, The Symphony of Primes, Distribution of Primes and Riemann’s Hypothesis, Xlibris Corporation,‎ (ISBN 978-1-4797-6558-4, lire en ligne), p. 18
  114. William Dunham, The Calculus Gallery: Masterpieces from Newton to Lebesgue, Princeton University Press,‎ (ISBN 978-0-691-09565-3, lire en ligne), p. 51
  115. Jean Jacquelin, Sophomore's Dream Function,‎ (lire en ligne)
  116. R. M. Abrarov and S. M. Abrarov, Properties and Applications of the Prime Detecting Function, arxiv.org,‎ (lire en ligne [PDF]), p. 8
  117. Henri Cohen, Number Theory: Volume II: Analytic and Modern Tools, Springer,‎ (ISBN 978-0-387-49893-5, lire en ligne), p. 127
  118. H. M. Srivastava,Choi Junesang, Series Associated With the Zeta and Related Functions, Kluwer Academic éditeurs,‎ (ISBN 0-7923-7054-6, lire en ligne), p. 30
  119. E. Catalan, Mémoire sur la transformation des séries, et sur quelques intégrales définies, Kluwer Academic éditeurs,‎ (lire en ligne), p. 618
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  121. (it) Mauro Fiorentini, Nielsen – Ramanujan (costanti di) (lire en ligne)
  122. Annie Cuyt, Vigdis Brevik Petersen, Brigitte Verdonk, Haakon Waadelantl, William B. Jones., Handbook of Continued Fractions for Special Functions, Springer,‎ (ISBN 978-1-4020-6948-2, lire en ligne), p. 188
  123. Helmut Brass,Knut Petras, Quadrature Theory: The Theory of Numerical Integration on a Compact Interval, AMS,‎ (ISBN 978-0-8218-5361-0, lire en ligne), p. 274
  124. Robin Whitty, Lieb’s Square Ice Theorem (lire en ligne [PDF])
  125. Eli Maor, e: The Story of a Number, Princeton University Press,‎ (ISBN 0-691-03390-0, lire en ligne)
  126. Robert Baillie, Summing The Curious Series of Kempner and Irwin, arxiv,‎ (lire en ligne [PDF]), p. 9
  127. Leonhard Euler, Consideratio quarumdam serierum, quae singularibus proprietatibus sunt praeditae,‎ (lire en ligne), p. 108
  128. Weisstein, Eric W, Gelfond-Schneider Constant, MathWorld (lire en ligne)
  129. Vijaya AV, Figuring Out Mathematics, Dorling Kindcrsley (India) Pvt. Lid.,‎ (ISBN 978-81-317-0359-5, lire en ligne), p. 15
  130. Chris De Corte, Fractal approximations to some famous constants,‎ (lire en ligne)
  131. (es) Número de bronce. Proporción de bronce (lire en ligne [PDF])
  132. M.R.Burns, Root constant, http://marvinrayburns.com/,‎ (lire en ligne)
  133. Richard E. Crandall, Unified algorithms for polylogarithm, L-series, and zeta variants, http://www.perfscipress.com,‎ (lire en ligne [PDF])
  134. Richard J. Mathar, Numerical Evaluation of the Oscillatory Integral, http://arxiv.org/abs/0912.3844,‎ (lire en ligne [PDF])
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  137. Gérard P. Michon, Numerical Constants,‎ (lire en ligne)
  138. Ian Stewart, Professor Stewart's Cabinet of Mathematical Curiosities, Birkhäuser Verlag,‎ (ISBN 978-1-84765-128-0, lire en ligne)
  139. H.M. Antia, Numerical Methods for Scientists and Engineers, Birkhäuser Verlag,‎ (ISBN 3-7643-6715-6, lire en ligne), p. 220
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Oeis Wiki[modifier | modifier le code]

Wolfram MathWorld[modifier | modifier le code]

  1. (en)Paper Folding Constant
  2. (en)Goh-Schmutz Constant
  3. (en)Totient Summatory Function
  4. (en)Fibonacci Factorial Constant
  5. (en)Koch Snowflake
  6. (en)Carlson-Levin Constant
  7. (en)Figure Eight Knot
  8. (en)Carefree Couple
  9. (en)Gausss Digamma Theorem
  10. (en)Copeland-Erdos Constant
  11. (en)Wallis's Constant
  12. (en)Relatively Prime
  13. (en)Renyi's Parking Constant
  14. (en)i
  15. (en)Polya's Random Walk Constant
  16. (en)Pascal's Triangle
  17. (en)Liouville's Constant
  18. a, b, c et d (en)Power Tower
  19. (en)Gompertz Constant
  20. (en)Silver Constant
  21. (en)Binomial Coefficient
  22. (en)Plouffe's Constant
  23. (en)Factorial Sums
  24. (en)Lemniscate Constant
  25. (en)Mills Constant
  26. (en)Lüroth's Constant
  27. (en)Niven's Constant
  28. (en)e
  29. (en)Kempner Series
  30. (en)Du Bois Reymond Constants
  31. a et b (en)Lebesgue Constants
  32. a et b (en)Foias Constant
  33. (en)Khinchin Harmonic Mean
  34. (en)Trott Constant
  35. (en)Wilbraham-Gibbs Constant
  36. (en)Grothendieck's Constant
  37. (en)Bifoliate
  38. (en)Murata's Constant
  39. (en)Dragon Curve
  40. (en)Gieseking's Constant
  41. (en)Gaussian Sum
  42. a et b (en)Riemann Zeta Function
  43. (en)Gamma Function
  44. (en)Artin's Constant
  45. (en)Lemniscate Case
  46. (en)Ramanujan Constant
  47. (en)Hyperbolic Tangent
  48. (en)Wallis Formula
  49. (en)Ford Circle
  50. (en)Gausss Constant
  51. (en)Delian Constant
  52. (en)Alladi-Grinstead Constant
  53. (en)Chaitin's Constant
  54. (en)Random Fibonacci Sequence
  55. (en)Lemniscate Constant
  56. (en)Porter's Constant
  57. (en)Fransen-Robinson Constant
  58. (en)Champernowne Constant
  59. (en)Golomb-Dickman
  60. (en)e
  61. (en)Backhouse's Constant
  62. (en)Sierpinski Constant
  63. (en)Omega Constant
  64. (en)Pythagorass Constant
  65. (en)Landau-Ramanujan Constant
  66. (en)Conway's Constant
  67. (en)Lévy Constant
  68. (en)Soldner's Constant
  69. (en)Hafner-Sarnak-McCurley Constant
  70. (en)Prime Products
  71. (en)Cahen's Constant
  72. (en)Laplace Limit
  73. (en)Gauss-Kuzmin-Wirsing Constant
  74. (en)Bernstein's Constant
  75. (en)Euler-Mascheroni Constant
  76. (en)Robbins Constant
  77. (en)Mertens Constant
  78. a et b (en)Feigenbaum Constant
  79. a et b (en)Brun's Constant
  80. (en)Tree Searching
  81. (en)Pi Formulas
  82. (en)Tree Weierstras's Constant
  83. (en)Glaisher-Kinkelin Constant
  84. a et b (en)Sophomores Dream
  85. (en)Twin Primes Constant
  86. (en)Natural Logarithm of 2
  87. (en)Catalan's Constant
  88. (en)Dirichlet Beta Function
  89. (en)Nielsen-Ramanujan Constants
  90. (en)Apery's Constant
  91. (en)Favard Constants
  92. (en)Lieb's Square Ice Constant
  93. (en)Riemann Zeta Function zeta(2)
  94. (en)Steiner's Problem
  95. (en)Erdos-Borwein Constant
  96. (en)Golden Ratio
  97. (en)Gelfond-Schneider Constant
  98. (en)Theodorus's Constant
  99. (en)Nested Radical Constant
  100. (en)Universal Parabolic Constant
  101. (en)Silver Ratio
  102. (en)MRB Constant
  103. (en)Levy Constant
  104. (en)Gelfonds Constant
  105. (en)Reciprocal Fibonacci Constant
  106. (en)Plastic Constant
  107. (en)Khinchin's Constant

Bibliographie[modifier | modifier le code]

  • Finch, Steven, Mathematical constants, Cambridge University Press,‎ (ISBN 3-540-67695-3)
  • Daniel Zwillinger, Standard Mathematical Tables and Formulae, Imperial College Press.,‎ (ISBN 978-1-4398-3548-7)
  • Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, Chapman & Hall/CRC,‎ (ISBN 1-58488-347-2)
  • Lloyd Kilford, Modular Forms, a Classical and Computational Introduction, Imperial College Press.,‎ (ISBN 978-1848162136)

Voir aussi[modifier | modifier le code]

Liens externes[modifier | modifier le code]