A173973 Decimal expansion of Zeta[2,1/3] - 2*Pi^2/3.

3, 5, 1, 5, 8, 6, 0, 8, 5, 8, 0, 3, 4, 1, 8, 8, 3, 3, 5, 9, 0, 2, 3, 4, 3, 4, 3, 3, 3, 0, 8, 4, 1, 5, 6, 0, 3, 6, 4, 3, 1, 0, 4, 5, 1, 4, 4, 5, 3, 7, 8, 4, 3, 9, 0, 9, 9, 9, 4, 5, 0, 2, 8, 3, 3, 5, 0, 9, 9, 1, 4, 3, 0, 9, 3, 2, 2, 8, 1, 9, 8, 1, 4, 1, 7, 9, 1, 3, 0, 6, 8, 7, 4, 4, 9, 4, 4, 3, 7, 4, 5, 9, 4, 6, 9

Offset: 1

Author

Artur Jasinski, Mar 03 2010

Keywords

• nonn
• cons

Comments

Zeta[s,a] is Mathematica's notation for the shifted Zeta-function Sum_{n>=1} 1/(n-a)^s. - R. J. Mathar, Jun 17 2016

Examples

			3.5158608...
		

Programs

Maple

Zeta(0,2,1/3)-2*Pi^2/3 ; evalf(%) ; # R. J. Mathar, Jun 17 2016

Mathematica

RealDigits[N[(Zeta[2, 1/3] - Zeta[2, 2/3])/2, 300]]

PARI

zetahurwitz(2,1/3)-2*Pi^2/3 \\ Charles R Greathouse IV, Jan 31 2018

Formula

Equals Zeta[2,1/3] - 2(Pi^2)/3 = 2(Pi^2)/3 - Zeta[2,2/3].

Extensions

Definition revised by N. J. A. Sloane, Aug 30 2011