cp's OEIS Frontend

A103133 Decimal expansion of Dirichlet series L_{-7}(2).

%I A103133 #27 Feb 16 2025 08:32:56
%S A103133 1,1,5,1,9,2,5,4,7,0,5,4,4,4,9,1,0,4,7,1,0,1,6,9,2,3,9,7,3,2,0,5,4,9,
%T A103133 9,6,4,7,9,7,8,2,1,4,0,4,6,8,6,5,6,6,9,1,4,0,8,3,9,6,8,6,3,6,1,6,6,1,
%U A103133 2,4,1,6,3,4,5,4,5,9,1,5,4,7,5,5,6,6,7,7,5,1,9,0,6,2,9,7,2,1,2,5,3,4
%N A103133 Decimal expansion of Dirichlet series L_{-7}(2).
%H A103133 D. Cvijovic, <a href="http://arxiv.org/abs/1011.0195">Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory</a>, arXiv:1011.0195 [math-ph], 2010.
%H A103133 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 98-99.
%H A103133 R. J. Mathar, <a href="https://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and prime zeta modulo functions for small moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015, L(m=7,r=4,s=2).
%H A103133 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletL-Series.html">Dirichlet L-Series</a>.
%F A103133 (Psi(1, 1/7) + Psi(1, 2/7) - Psi(1, 3/7) + Psi(1, 4/7) - Psi(1, 5/7) - Psi(1, 6/7))/49, where Psi(1, x) is the polygamma function of order 1.
%F A103133 Equals Sum_{n>=1} A175629(n)/n^2. - _R. J. Mathar_, Jan 15 2021
%F A103133 Equals 1/(Product_{p prime == 1, 2 or 4 (mod 7)} (1 - 1/p^2) * Product_{p prime == 3, 5 or 6 (mod 7)} (1 + 1/p^2)). - _Amiram Eldar_, Dec 17 2023
%e A103133 1.151925470544491047...
%t A103133 (PolyGamma[1, 1/7] + PolyGamma[1, 2/7] - PolyGamma[1, 3/7] + PolyGamma[1, 4/7] - PolyGamma[1, 5/7] - PolyGamma[1, 6/7])/49 // RealDigits[#, 10, 102]& // First
%Y A103133 Cf. A326919, A327135.
%K A103133 nonn,cons
%O A103133 1,3
%A A103133 _Eric W. Weisstein_, Jan 23 2005
%E A103133 Formula updated by _Jean-François Alcover_, Apr 01 2015