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A094692
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Decimal expansion of 2^(5/4)*sqrt(Pi)*exp(Pi/8)/Gamma(1/4)^2.
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1
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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
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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Michel Waldschmidt, Elliptic functions and transcendance, Surveys in number theory, 143-188, Dev. Math., 17, Springer, New York, 2008.
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LINKS
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FORMULA
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c = 2^(5/4)*Pi^(1/2)*exp(Pi/8)/Gamma(1/4)^2.
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EXAMPLE
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0.474949379987920650332...
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MATHEMATICA
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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 *)
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PROG
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(PARI) 2^(5/4)*Pi^(1/2)*exp(Pi/8)/gamma(1/4)^2 \\ _Benoit Cloitre_, Jan 07 2006
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CROSSREFS
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KEYWORD
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AUTHOR
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_Robert G. Wilson v_, May 19 2004
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EXTENSIONS
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Edited by _N. J. A. Sloane_, Aug 19 2008 at the suggestion of _R. J. Mathar_
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STATUS
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approved
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