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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
Michel Waldschmidt, Elliptic Functions and Transcendence, preprint, Corollary 49.
Eric Weisstein's World of Mathematics, Weierstrass Constant.
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
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.)