OFFSET
0,3
LINKS
Eric Weisstein's MathWorld, Multivariate Zeta Function
Wikipedia, Multiple zeta function
FORMULA
zetamult(6,2) = Sum_{m>=2} (sum_{n=1..m-1} 1/(m^6*n^2)).
Equals Sum_{m>=2} H(m-1, 2)/m^6, where H(n,2) is the n-th harmonic number of order 2.
EXAMPLE
0.01781974041683598836265953024872461216871313711029118841882136191761348...
MATHEMATICA
digits = 99; zetamult[6, 2] = NSum[HarmonicNumber[m-1, 2]/m^6, {m, 2, Infinity}, WorkingPrecision -> digits+20, NSumTerms -> 200, Method -> {"NIntegrate", "MaxRecursion" -> 18}]; Join[{0}, RealDigits[zetamult[6, 2], 10, digits] // First]
PROG
(PARI) zetamult([6, 2]) \\ Charles R Greathouse IV, Jan 21 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jun 15 2015
STATUS
approved