A238135 Decimal expansion of Euler's Multi-Zeta Sum S(2,3) = Sum_{n >= 1} (Sum_{k=1..n}((-1)^(k + 1)/k)^2/(n + 1)^3).

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

Offset

0,2

Links

Table of n, a(n) for n=0..99.

D. H. Bailey and J. M. Borwein, Euler's Multi-Zeta Sums, Lawrence Berkeley National Laboratory, 1995, p. 10.

Example

0.1561669333811769158810359096879881936857767...

Mathematica

4*PolyLog[5, 1/2] - 1/30*Log[2]^5 - 17/32*Zeta[5] - 11/720*Pi^4*Log[2] + 7/4*Zeta[3]*Log[2]^2 + 1/18*Pi^2*Log[2]^3 - 1/8*Pi^2*Zeta[3] // RealDigits[#, 10, 100]& // First

Prog

(PARI) 4*polylog(5, 1/2)-1/30*log(2)^5-17/32*zeta(5) - 11/720*Pi^4*log(2) + 7/4*zeta(3)*log(2)^2 + 1/18*Pi^2*log(2)^3 - 1/8*Pi^2*zeta(3) \\ Charles R Greathouse IV, Jul 18 2014
(SageMath)
RR = RealBallField(380)
f = fast_callable(4*polylog(5, 1/2) - 1/30*log(2)^5 - 17/32*zeta(5) - 11/720*pi^4*log(2) + 7/4*zeta(3)*log(2)^2 + 1/18*pi^2*log(2)^3 - 1/8*pi^2*zeta(3), vars=[x], domain=RR)
print([int(t) for t in str(f(0))[3:103]]) # Peter Luschny, May 06 2020

Crossrefs

Cf. A218505.

Sequence in context: A222133 A198728 A345144 * A195449 A020798 A374002

Adjacent sequences: A238132 A238133 A238134 * A238136 A238137 A238138

Keyword

nonn,cons

Author

Jean-François Alcover, Feb 18 2014

Status

approved