A197110 Decimal expansion of Pi^4/120.

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

Offset: 0

Author

R. J. Mathar, Oct 10 2011

Keywords

• cons
• nonn
• easy

Comments

Decimal expansion of the double zeta function zeta(2,2). Not to be confused with the Hurwitz zeta function of two arguments or with the second derivative of the Riemann zeta function.

Examples

			0.8117424... = A164109/40 .
		

Links

• R. E. Crandall and J. P. Buhler, On the evaluation of Euler sums, Exper. Math. 3 (1994), 275.
• Wikipedia, Multiple zeta function
• Index entries for transcendental numbers

Crossrefs

Cf. A092425, A164109.

Programs

Maple

evalf(Pi^4/120) ;

Mathematica

First[RealDigits[Pi^4/120,10,100]] (* Geoffrey Critzer, Nov 03 2013 *)

PARI

Pi^4/120 \\ Charles R Greathouse IV, Apr 17 2015

PARI

zetamult([2,2]) \\ Charles R Greathouse IV, Apr 17 2015

Formula

Equals Sum_{n >=2} Sum_{m=1..n-1} 1/(n*m)^2.

Extensions

More terms from D. S. McNeil, Oct 10 2011

Definition simplified by R. J. Mathar, Feb 05 2013