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A105372
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Decimal expansion of Hypergeometric2F1[ -(1/4),3/4,1,1] = sqrt(Pi)/(Gamma[1/4]*Gamma[5/4]).
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3
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5, 3, 9, 3, 5, 2, 6, 0, 1, 1, 8, 8, 3, 7, 9, 3, 5, 6, 6, 6, 7, 9, 3, 5, 7, 2, 2, 3, 5, 5, 5, 5, 2, 7, 3, 2, 7, 6, 5, 8, 6, 8, 9, 6, 5, 4, 4, 3, 0, 4, 0, 1, 3, 0, 3, 3, 9, 9, 4, 6, 6, 3, 1, 8, 6, 3, 8, 8, 2, 9, 8, 8, 4, 8, 6, 5, 1, 5, 6, 8, 2, 8, 1, 5, 5, 9, 2, 1, 3, 7, 2, 2, 7, 5, 3, 3, 7, 7, 1, 4
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OFFSET
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0,1
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COMMENTS
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This constant appears in solution to an ODE considered in A104996, A104997.
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LINKS
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FORMULA
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Hypergeometric2F1[ -(1/4), 3/4, 1, 1] = Sqrt[Pi]/(Gamma[1/4]*Gamma[5/4]).
4*sqrt(Pi)/Gamma(1/4)^2.
1 / EllipticK(1/sqrt(2)) (Maple notation).
1 / EllipticK[1/2] (Mathematica notation).
(End)
Equals Product_{k>=1} (1 + (-1)^k/(2*k)). - Amiram Eldar, Aug 26 2020
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EXAMPLE
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0.53935260118837935666793572235555273276586896544304013033994...
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MAPLE
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MATHEMATICA
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PROG
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(PARI) sqrt(Pi)/(gamma(1/4)*gamma(5/4)) \\ G. C. Greubel, Jan 09 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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