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A078127 DirichletBeta'[1]. 0

%I

%S 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,

%T 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,

%U 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

%N DirichletBeta'[1].

%C (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.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 8.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>

%F Equals Sum_{k>=1} (-1)^(k+1)*log(2*k+1)/(2*k+1). - _Jean-Fran├žois Alcover_, Aug 11 2014

%e 0.192901316796912429..

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

%Y Cf. A068465, A068466.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Nov 19 2002

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Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)