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A241421 Decimal expansion of D(1), where D(x) is the infinite product function defined in the formula section (or in the Finch reference). 3
2, 2, 3, 5, 8, 8, 5, 5, 9, 5, 5, 0, 8, 9, 6, 9, 8, 6, 4, 2, 8, 3, 9, 6, 4, 7, 9, 9, 3, 1, 1, 8, 9, 0, 6, 4, 4, 8, 4, 5, 1, 5, 9, 1, 2, 2, 8, 5, 9, 5, 2, 4, 7, 4, 7, 7, 9, 3, 4, 4, 7, 9, 7, 8, 2, 6, 0, 6, 2, 7, 0, 8, 1, 4, 5, 7, 2, 5, 2, 2, 1, 7, 9, 3, 2, 8, 3, 2, 0, 2, 9, 5, 2, 8, 3, 2, 3, 4, 6, 2, 8, 9, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 136.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 20.

Eric Weisstein's MathWorld, Barnes G-Function

Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant

FORMULA

D(x) = lim_{n->infinity} ( Prod_{k=1..2n+1} (1+x/k)^((-1)^(k+1)*k) ).

D(x) = (e^(x/2-1/4)*A^3*G((x+1)/2)^2*Gamma(x/2)^(x-2)*Gamma((x+1)/2)^(1-x)*(Gamma((x+1)/2)/Gamma(x/2))^x)/(2^(1/12)*G(x/2)^2), where A is the Glaisher-Kinkelin constant and G is the Barnes G-function.

D(1) = A^6/(2^(1/6)*sqrt(Pi)).

EXAMPLE

2.23588559550896986428396479931189064484515912285952474779344797826...

MATHEMATICA

RealDigits[Glaisher^6/(2^(1/6)*Sqrt[Pi]), 10, 104] // First

PROG

(PARI) default(realprecision, 100); A=exp(1/12-zeta'(-1)); A^6/(2^(1/6)* sqrt(Pi)) \\ G. C. Greubel, Aug 24 2018

CROSSREFS

Cf. A006752, A019610 (D(2)), A074962, A241420 (D(1/2)).

Sequence in context: A127678 A199962 A114990 * A157176 A276429 A111181

Adjacent sequences:  A241418 A241419 A241420 * A241422 A241423 A241424

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Aug 08 2014

STATUS

approved

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Last modified March 6 06:25 EST 2021. Contains 341842 sequences. (Running on oeis4.)