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A247670
Decimal expansion of Sum_{n >= 0} (-1)^n*H(n)/(2n+1)^3, where H(n) is the n-th harmonic number.
1
0, 2, 8, 5, 7, 4, 1, 7, 0, 6, 3, 6, 2, 4, 3, 5, 9, 0, 9, 9, 9, 0, 8, 4, 2, 9, 5, 1, 2, 5, 0, 4, 4, 3, 1, 0, 8, 8, 6, 0, 3, 0, 1, 8, 6, 9, 1, 4, 8, 6, 0, 1, 6, 0, 9, 1, 3, 3, 1, 9, 3, 5, 0, 9, 8, 8, 4, 9, 8, 4, 2, 4, 1, 7, 2, 1, 7, 2, 9, 5, 1, 6, 9, 9, 9, 7, 3, 8, 0, 5, 8, 8, 2, 1, 2, 4, 9, 0, 1, 2, 4, 1
OFFSET
0,2
LINKS
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) p. 34.
FORMULA
Equals -(Pi^3/16)*log(2) - (7*Pi/16)*zeta(3) + (1/512)*(PolyGamma(3, 1/4) - PolyGamma(3, 3/4)), where PolyGamma(n,z) gives the n-th derivative of the digamma function Psi^(n)(z).
EXAMPLE
-0.02857417063624359099908429512504431088603018691486...
MATHEMATICA
s = -(Pi^3/16)*Log[2] - (7*Pi/16)*Zeta[3] + (1/512)*(PolyGamma[3, 1/4] - PolyGamma[3, 3/4]); Join[{0}, RealDigits[s, 10, 101] // First]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved