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A097676
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Decimal expansion of the constant 8*exp(psi(7/8) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.
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15
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6, 3, 7, 6, 6, 3, 2, 4, 8, 9, 4, 1, 6, 6, 7, 7, 8, 5, 5, 0, 0, 1, 7, 6, 2, 5, 9, 3, 8, 2, 5, 1, 0, 7, 9, 0, 6, 2, 6, 7, 4, 3, 5, 3, 2, 6, 7, 8, 6, 4, 6, 2, 1, 6, 7, 6, 7, 3, 0, 6, 4, 1, 0, 7, 4, 3, 4, 2, 6, 4, 5, 4, 9, 1, 5, 2, 5, 9, 9, 9, 3, 9, 0, 8, 8, 3, 3, 7, 3, 3, 1, 6, 4, 3, 8, 3, 2, 7, 6, 5, 5, 5, 3, 4, 9
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OFFSET
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1,1
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COMMENTS
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This constant appears in Benoit Cloitre's generalized Euler-Gauss formula for the Gamma function (see Cloitre link) and is involved in the exact determination of asymptotic limits of certain order-8 linear recursions with varying coefficients (see A097682 for example).
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REFERENCES
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A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.
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LINKS
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FORMULA
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c = (1+sqrt(2))^(-sqrt(2))/2*exp(Pi/2*(1+sqrt(2))).
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EXAMPLE
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c = 6.37663248941667785500176259382510790626743532678646216767306...
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MATHEMATICA
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RealDigits[(1 + Sqrt[2])^(-Sqrt[2])/2E^(Pi/2*(1 + Sqrt[2])), 10, 105][[1]] (* Robert G. Wilson v, Aug 27 2004 *)
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PROG
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(PARI) 8*exp(psi(7/8)+Euler)
(Magma) SetDefaultRealField(RealField(100)); R:= RealField();
(1+Sqrt(2))^(-Sqrt(2))/2*Exp(Pi(R)/2*(1+Sqrt(2))); // G. C. Greubel, Sep 07 2018
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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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