A094692 Decimal expansion of 2^(5/4)*sqrt(Pi)*exp(Pi/8)/Gamma(1/4)^2.

4, 7, 4, 9, 4, 9, 3, 7, 9, 9, 8, 7, 9, 2, 0, 6, 5, 0, 3, 3, 2, 5, 0, 4, 6, 3, 6, 3, 2, 7, 9, 8, 2, 9, 6, 8, 5, 5, 9, 5, 4, 9, 3, 7, 3, 2, 1, 7, 2, 0, 2, 9, 8, 2, 2, 8, 3, 3, 3, 1, 0, 2, 4, 8, 6, 4, 5, 5, 7, 9, 2, 9, 1, 7, 4, 8, 8, 3, 8, 6, 0, 2, 7, 4, 2, 7, 5, 6, 4, 1, 2, 5, 0, 5, 0, 2, 1, 4, 4, 4, 1, 8, 9, 0, 3

Offset

0,1

Comments

Decimal expansion of sigma(1|1,i)/2, where sigma is the Weierstrass sigma function and 1 and i are the half-periods. - Eric W. Weisstein, Jan 15 2005

Known to be transcendental. - Benoit Cloitre, Jan 07 2006

Called "Weierstrass constant" after the German mathematician Karl Theodor Wilhelm Weierstrass (1815-1897). - Amiram Eldar, Jun 24 2021

References

Michel Waldschmidt, Elliptic functions and transcendance, Surveys in number theory, 143-188, Dev. Math., 17, Springer, New York, 2008.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Simon Plouffe, 2**(5/4)*sqrt(Pi)*exp(Pi/8)*GAMMA(1/4)**(-2).

Michel Waldschmidt, Elliptic Functions and Transcendence, preprint, Corollary 49.

Eric Weisstein's World of Mathematics, Weierstrass Constant.

Index entries for transcendental numbers

Formula

c = 2^(5/4)*Pi^(1/2)*exp(Pi/8)/Gamma(1/4)^2.

Example

0.474949379987920650332...

Mathematica

RealDigits[2^(5/4) Sqrt[Pi] E^(Pi/8)/Gamma[1/4]^2, 10, 111][[1]]
RealDigits[N[WeierstrassSigma[1, WeierstrassInvariants[{1, I}]]/2, 100], 10][[1]] (* Eric W. Weisstein, Apr 16 2018 *)

Prog

(PARI) 2^(5/4)*Pi^(1/2)*exp(Pi/8)/gamma(1/4)^2 \\ Benoit Cloitre, Jan 07 2006

Crossrefs

Sequence in context: A170863 A021682 A242187 * A059139 A329740 A110669

Adjacent sequences: A094689 A094690 A094691 * A094693 A094694 A094695

Keyword

cons,nonn

Author

Robert G. Wilson v, May 19 2004

Extensions

Edited by N. J. A. Sloane, Aug 19 2008 at the suggestion of R. J. Mathar

Status

approved