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Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,3).
(history; published version)

#10 by Charles R Greathouse IV at Thu Jan 21 14:44:26 EST 2016

CROSSREFS

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258985 (5,2), A258497 A258947 (6,2), A258986 (2,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

Discussion

Thu Jan 21

14:44

OEIS Server: https://oeis.org/edit/global/2482

#9 by Charles R Greathouse IV at Thu Jan 21 14:39:54 EST 2016

STATUS

editing

approved

#8 by Charles R Greathouse IV at Thu Jan 21 14:39:51 EST 2016

PROG

(PARI) zetamult([3, 3]) \\ Charles R Greathouse IV, Jan 21 2016

STATUS

approved

editing

#7 by N. J. A. Sloane at Tue Jun 16 13:34:17 EDT 2015

STATUS

proposed

approved

#6 by Jean-François Alcover at Tue Jun 16 08:26:40 EDT 2015

STATUS

editing

proposed

#5 by Jean-François Alcover at Tue Jun 16 08:26:30 EDT 2015

FORMULA

zetamult(3,3) = Sum_{m>=2..infinity} (Sum_{n=1..m-1} 1/(m^2*n^3)) = (9/2)*zeta(5) - 2*zeta(2)*zeta(3).

STATUS

proposed

editing

#4 by Jean-François Alcover at Tue Jun 16 04:36:48 EDT 2015

STATUS

editing

proposed

#3 by Jean-François Alcover at Tue Jun 16 04:36:38 EDT 2015

CROSSREFS

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258985 (5,2), A258497 (6,2), A258986 (2,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

#2 by Jean-François Alcover at Tue Jun 16 04:24:58 EDT 2015

NAME

allocated for Jean-François Alcover

Decimal expansion of the multiple zeta value (Euler sum) zetamult(3,3).

DATA

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

OFFSET

0,1

LINKS

Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>

Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiple_zeta_function">Multiple zeta function</a>

FORMULA

zetamult(3,3) = Sum_{m=2..infinity} (Sum_{n=1..m-1} 1/(m^2*n^3)) = (9/2)*zeta(5) - 2*zeta(2)*zeta(3).

EXAMPLE

0.213798868224592547099583574508033649640958957865517556144512748947...

MATHEMATICA

RealDigits[(9/2)*Zeta[5] - 2*Zeta[2]*Zeta[3], 10, 103] // First

CROSSREFS

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)),A258984 (4,2), A258985 (5,2), A258497 (6,2), A258986 (2,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

KEYWORD

allocated

nonn,cons,easy

AUTHOR

Jean-François Alcover, Jun 16 2015

STATUS

approved

editing

#1 by Jean-François Alcover at Tue Jun 16 04:04:22 EDT 2015

NAME

allocated for Jean-François Alcover

KEYWORD

allocated

STATUS

approved