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A078127
DirichletBeta'[1].
2
1, 9, 2, 9, 0, 1, 3, 1, 6, 7, 9, 6, 9, 1, 2, 4, 2, 9, 3, 6, 3, 1, 8, 9, 7, 6, 4, 0, 2, 8, 0, 3, 2, 7, 8, 5, 2, 4, 5, 0, 9, 6, 8, 6, 7, 6, 2, 0, 0, 0, 7, 5, 2, 7, 1, 7, 1, 3, 4, 9, 2, 2, 7, 4, 4, 3, 6, 0, 5, 7, 0, 3, 5, 9, 2, 7, 7, 8, 7, 7, 0, 3, 9, 1, 4, 4, 3, 0, 5, 5, 1, 6, 3, 8, 7, 8, 4, 6, 0, 4, 7
OFFSET
0,2
COMMENTS
(Pi/4)*(gamma + log[2*Pi] - 2*log(Gamma(1/4)/Gamma(3/4))), where gamma is Euler's constant and Gamma(x) is the Euler Gamma function.
LINKS
Eric Weisstein's World of Mathematics, Dirichlet Beta Function
FORMULA
Equals Sum_{k>=1} (-1)^(k+1)*log(2*k+1)/(2*k+1). - Jean-François Alcover, Aug 11 2014
EXAMPLE
0.192901316796912429..
MAPLE
Pi/4*(gamma+log(2*Pi)-2*log(GAMMA(1/4)/GAMMA(3/4))); evalf(%) ; # R. J. Mathar, Jun 10 2024
MATHEMATICA
Prepend@@RealDigits[(Pi*(EulerGamma + 2*Log[2] + 3*Log[Pi] - 4*Log[Gamma[1/4]]))/4, 10, 101]
CROSSREFS
Sequence in context: A073007 A157215 A021919 * A348870 A217626 A275362
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Nov 19 2002
STATUS
approved