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

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, 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, 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

Offset: 0

Author

R. J. Mathar, Jul 20 2012

Keywords

• cons
• nonn

Comments

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

Examples

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

Links

• R. J. Mathar, Table of Dirichlet L-series and prime zeta modulo functions for small moduli, arXiv:10008.2547 [math.NT], 2010-2015, Table in section 2.2, value at m=6, r=2, s=2.

Crossrefs

Cf. A086724, A086722, A100044.

Programs

Maple

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

Mathematica

RealDigits[ (PolyGamma[1, 1/6] - PolyGamma[1, 5/6])/36, 10, 105] // First  (* Jean-François Alcover, Feb 11 2013, after R. J. Mathar *)

Formula

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.

Equals A173973 / 3.6 . - R. J. Mathar, Jun 02 2016

Extensions

More terms from Jean-François Alcover, Feb 11 2013