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A214552 Decimal expansion of the Dirichlet L-series of the non-principal character mod 6 evaluated at s=2. 3

%I #19 Aug 25 2021 13:39:30

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

%C The non-principal character is A134667. The constant is sum_{n>=1} A134667(n)/n^s with s=2.

%H 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 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 Equals A173973 / 3.6 . - _R. J. Mathar_, Jun 02 2016

%e 0.97662801612060787108398...= 1/1^2 -1/5^2 +1/7^2 -1/11^2 + 1/13^2 -1/17^2 +-...

%p evalf( (Psi(1,1/6)-Psi(1,5/6))/36) ;

%t RealDigits[ (PolyGamma[1, 1/6] - PolyGamma[1, 5/6])/36, 10, 105] // First (* _Jean-François Alcover_, Feb 11 2013, after _R. J. Mathar_ *)

%Y Cf. A086724, A086722, A100044.

%K cons,nonn

%O 0,1

%A _R. J. Mathar_, Jul 20 2012

%E More terms from _Jean-François Alcover_, Feb 11 2013

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