This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078127 #30 Jun 17 2025 19:24:21
%S A078127 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 A078127 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 A078127 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 A078127 Decimal expansion of DirichletBeta'(1).
%H A078127 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 8.
%H A078127 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>
%F A078127 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.
%F A078127 Equals Sum_{k>=1} (-1)^(k+1)*log(2*k+1)/(2*k+1). - _Jean-François Alcover_, Aug 11 2014
%e A078127 0.1929013167969124293631897640...
%p A078127 Pi/4*(gamma+log(2*Pi)-2*log(GAMMA(1/4)/GAMMA(3/4))); evalf(%) ; # _R. J. Mathar_, Jun 10 2024
%t A078127 Prepend@@RealDigits[(Pi*(EulerGamma + 2*Log[2] + 3*Log[Pi] - 4*Log[Gamma[1/4]]))/4, 10, 101]
%Y A078127 Cf. A000796, A001620, A068465, A068466.
%K A078127 nonn,cons
%O A078127 0,2
%A A078127 _Eric W. Weisstein_, Nov 19 2002