A078127 Decimal expansion of 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

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 (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.

Equals Sum_{k>=1} (-1)^(k+1)*log(2*k+1)/(2*k+1). - Jean-François Alcover, Aug 11 2014

Example

0.1929013167969124293631897640...

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

Cf. A000796, A001620, A068465, A068466.

Sequence in context: A073007 A157215 A021919 * A383188 A348870 A217626

Adjacent sequences: A078124 A078125 A078126 * A078128 A078129 A078130

Keyword

nonn,cons

Author

Eric W. Weisstein, Nov 19 2002

Status

approved