OFFSET
0,1
COMMENTS
Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.47 gives Pi*sqrt(3)*(psi(2/3)-psi(1/3))/72-Zeta(3)/3 which is negative and therefore not correct.
Comment from Mikhail Kalmykov (kalmykov.mikhail(AT)googlemail.com), Jun 01 2009: Analytical results for this sum were also given in Eq. (8) of the Kalmykov and Veretin paper. These results confirm the last comment from Alois P. Heinz.
LINKS
J. M. Borwein, R. Girgensohn, Evaluation of Binomial Series, CECM-02-188 (2002).
A. I. Davydychev, M. Yu. Kalmykov, Massive Feynman diagrams and inverse binomial sums, Nucl. Phys. B 699 (2004), 3-64.
M. Yu. Kalmykov and O. Veretin, Single-scale diagrams and multiple binomial sums, Phys. Lett. B 483 (2000) 315-323.
R. J. Mathar, Corrigenda to "Interesting Series involving..", arXiv:0905.0215 [math.CA]
FORMULA
Comment from Alois P. Heinz, Feb 08 2009: Maple's answer to this is: a:= sum(1/(n^3*binomial(2*n,n)), n=1..infinity); a:= 1/2 hypergeom([1, 1, 1, 1], [2, 2, 3/2], 1/4); evalf (a, 140); .522946192133335108491185183527303540163044591743977841465941014...
EXAMPLE
0.522946...
MATHEMATICA
RealDigits[ N[1/18*(Sqrt[3]* Pi*(-PolyGamma[1, 2/3] + PolyGamma[1, 4/3] + 9) - 24*Zeta[3]), 105]][[1]] (* Jean-François Alcover, Nov 08 2012, after R. J. Mathar *)
CROSSREFS
KEYWORD
AUTHOR
R. J. Mathar, Feb 08 2009
STATUS
approved