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A258947
Decimal expansion of the multiple zeta value (Euler sum) zetamult(6,2).
10
0, 1, 7, 8, 1, 9, 7, 4, 0, 4, 1, 6, 8, 3, 5, 9, 8, 8, 3, 6, 2, 6, 5, 9, 5, 3, 0, 2, 4, 8, 7, 2, 4, 6, 1, 2, 1, 6, 8, 7, 1, 3, 1, 3, 7, 1, 1, 0, 2, 9, 1, 1, 8, 8, 4, 1, 8, 8, 2, 1, 3, 6, 1, 9, 1, 7, 6, 1, 3, 4, 8, 0, 2, 7, 6, 4, 1, 6, 0, 4, 6, 3, 7, 1, 8, 2, 8, 6, 2, 1, 0, 1, 9, 2, 0, 5, 8, 7, 9, 4
OFFSET
0,3
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
Sequence in context: A329219 A093720 A154216 * A360381 A216207 A171274
KEYWORD
nonn,cons
AUTHOR
STATUS
approved