A078127 DirichletBeta'[1].

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

Table of n, a(n) for n=0..100.

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..

Mathematica

Prepend@@RealDigits[(Pi*(EulerGamma + 2*Log[2] + 3*Log[Pi] - 4*Log[Gamma[1/4]]))/4, 10, 101]

Crossrefs

Cf. A068465, A068466.

Sequence in context: A073007 A157215 A021919 * A348870 A217626 A275362

Adjacent sequences: A078124 A078125 A078126 * A078128 A078129 A078130

Keyword

nonn,cons

Author

Eric W. Weisstein, Nov 19 2002

Status

approved