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
Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 8.
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Nov 19 2002
STATUS
approved