cp's OEIS Frontend

A261624 Decimal expansion of the Dirichlet beta function at 1/5.

%I A261624 #15 Feb 16 2025 08:33:26
%S A261624 5,7,3,7,1,0,8,4,7,1,8,5,9,4,6,6,4,9,3,5,7,2,6,6,5,2,7,8,3,2,0,0,4,1,
%T A261624 7,0,4,3,6,2,4,6,9,3,8,2,4,2,6,9,0,9,3,7,6,1,8,9,5,3,6,2,8,2,5,0,7,9,
%U A261624 2,5,3,6,1,1,2,6,5,9,4,2,1,5,7,5,0,6,2,8,3,0,1,9,3,3,1,7,4,2,4,8,8,1
%N A261624 Decimal expansion of the Dirichlet beta function at 1/5.
%H A261624 G. C. Greubel, <a href="/A261624/b261624.txt">Table of n, a(n) for n = 0..10000</a>
%H A261624 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>
%H A261624 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_beta_function">Dirichlet beta function</a>
%F A261624 beta(1/5) = (zeta(1/5, 1/4) - zeta(1/5, 3/4))/2^(2/5).
%e A261624 0.57371084718594664935726652783200417043624693824269093761895362825...
%p A261624 evalf(Sum((-1)^n/(2*n+1)^(1/5), n=0..infinity), 120); # _Vaclav Kotesovec_, Aug 27 2015
%t A261624 RealDigits[DirichletBeta[1/5],10,102]//First
%o A261624 (PARI) beta(x)=(zetahurwitz(x, 1/4)-zetahurwitz(x, 3/4))/4^x
%o A261624 beta(.2) \\ _Charles R Greathouse IV_, Oct 18 2024
%Y A261624 Cf. A003881 (beta(1)=Pi/4), A006752 (beta(2)=Catalan), A153071 (beta(3)), A175572 (beta(4)), A175571 (beta(5)), A175570 (beta(6)), A261622 (beta(1/3)), A261623 (beta(1/4)).
%K A261624 nonn,cons,easy
%O A261624 0,1
%A A261624 _Jean-François Alcover_, Aug 27 2015