A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

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

Links

Table of n, a(n) for n=0..99.

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 8.

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

Cf. A203142, A203143, A203144, A203146.

Sequence in context: A131360 A338780 A213714 * A353612 A368243 A259657

Adjacent sequences: A242008 A242009 A242010 * A242012 A242013 A242014

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 11 2014

Status

approved