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A242011
Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).
2
0, 2, 3, 0, 0, 4, 5, 8, 7, 8, 6, 2, 7, 3, 6, 0, 1, 0, 3, 1, 7, 9, 9, 2, 6, 0, 2, 1, 4, 5, 1, 4, 6, 9, 6, 2, 3, 1, 8, 6, 6, 7, 6, 4, 1, 4, 7, 5, 0, 8, 8, 3, 2, 9, 0, 9, 6, 3, 8, 0, 0, 6, 2, 0, 6, 5, 8, 1, 4, 5, 4, 7, 6, 3, 5, 4, 5, 5, 9, 4, 1, 4, 0, 3, 1, 5, 6, 6, 2, 3, 6, 1, 5, 5, 8, 9, 1, 9, 6, 7
OFFSET
0,2
FORMULA
(Pi/(2*sqrt(3)))*(log(Gamma(1/8)/Gamma(3/8)/(Gamma(5/8)/Gamma(7/8))) - (gamma + log(2*Pi))), where gamma is Euler's constant and Gamma(x) is the Euler Gamma function.
EXAMPLE
0.02300458786273601031799260214514696231866764147508832909638...
MATHEMATICA
s = (Pi/(2*Sqrt[2]))*(Log[Gamma[1/8]*Gamma[3/8]/(Gamma[5/8]*Gamma[7/8])] - (EulerGamma + Log[2*Pi])); Join[{0}, RealDigits[s, 10, 99] // First]
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved