cp's OEIS Frontend

A214552 Decimal expansion of the Dirichlet L-series of the non-principal character mod 6 evaluated at s=2.

%I A214552 #19 Aug 25 2021 13:39:30
%S A214552 9,7,6,6,2,8,0,1,6,1,2,0,6,0,7,8,7,1,0,8,3,9,8,4,2,8,7,0,3,0,1,1,5,4,
%T A214552 4,5,4,5,6,4,1,7,9,2,0,6,8,1,6,0,6,7,7,5,2,7,7,6,2,5,0,7,8,7,0,8,6,0,
%U A214552 8,7,3,0,8,1,4,5,2,2,7,7,2,6,1,6,0,8,6,9,6,3,5,4,0,2,6,2,3,2,6,2,7,6,3,0,2
%N A214552 Decimal expansion of the Dirichlet L-series of the non-principal character mod 6 evaluated at s=2.
%C A214552 The non-principal character is A134667. The constant is sum_{n>=1} A134667(n)/n^s with s=2.
%H A214552 R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and prime zeta modulo functions for small moduli</a>, arXiv:10008.2547 [math.NT], 2010-2015, Table in section 2.2, value at m=6, r=2, s=2.
%F A214552 Equals 2/3*4F3(1/2,1,1,2; 5/4,3/2,7/4; 3/4), where 4F3 is the generalized hypergeometric function. - _Jean-François Alcover_, Dec 16 2014, after _R. J. Mathar_.
%F A214552 Equals A173973 / 3.6 . - _R. J. Mathar_, Jun 02 2016
%e A214552 0.97662801612060787108398...= 1/1^2 -1/5^2 +1/7^2 -1/11^2 + 1/13^2 -1/17^2 +-...
%p A214552 evalf( (Psi(1,1/6)-Psi(1,5/6))/36) ;
%t A214552 RealDigits[ (PolyGamma[1, 1/6] - PolyGamma[1, 5/6])/36, 10, 105] // First  (* _Jean-François Alcover_, Feb 11 2013, after _R. J. Mathar_ *)
%Y A214552 Cf. A086724, A086722, A100044.
%K A214552 cons,nonn
%O A214552 0,1
%A A214552 _R. J. Mathar_, Jul 20 2012
%E A214552 More terms from _Jean-François Alcover_, Feb 11 2013