|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|