

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
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OFFSET

1,1


REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 GlaisherKinkelin 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.
Steven R. Finch, Errata and Addenda to Mathematical Constants [Cached copy, with permission of the author]
Eric Weisstein's MathWorld, Barnes GFunction
Eric Weisstein's MathWorld, GlaisherKinkelin Constant


FORMULA

D(x) = lim_{n>infinity} ( Prod_{k=1..2n+1} (1+x/k)^((1)^(k+1)*k) ).
D(x) = (e^(x/21/4)*A^3*G((x+1)/2)^2*Gamma(x/2)^(x2)*Gamma((x+1)/2)^(1x)*(Gamma((x+1)/2)/Gamma(x/2))^x)/(2^(1/12)*G(x/2)^2), where A is the GlaisherKinkelin constant and G is the Barnes Gfunction.
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(1/12zeta'(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

JeanFrançois Alcover, Aug 08 2014


STATUS

approved



