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 A094692 Decimal expansion of 2^(5/4)*sqrt(Pi)*exp(Pi/8)/Gamma(1/4)^2. 1
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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

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Last modified February 28 04:16 EST 2024. Contains 370379 sequences. (Running on oeis4.)