A247670 Decimal expansion of Sum_{n >= 0} (-1)^n*H(n)/(2n+1)^3, where H(n) is the n-th harmonic number.
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
Examples
-0.02857417063624359099908429512504431088603018691486...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) p. 34.
Programs
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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]
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).