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F(1) = 7*Zeta(3)/16 = Sum_{r>=1} (1+1/3+1/5+..+1/(2r-1))/r^2 = 0.525899895... [Coppo] - R. J. Mathar, Jun 13 2024
F(1) = 7*Zeta(3)/16 = Sum_{r>=1} (1+1/3+1/5+1/(2r-1))/r^2 = 0.525899895... [Coppo] - R. J. Mathar, Jun 13 2024
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Marc-Antoine Coppo and Bernard Candelpergher, <a href="http://dx.doi.org/10.1016/j.jnjnt.2014.11.007">Inverse binomial series and values of Arakawa-Kaneko zeta functions</a>, J. Number Theory 150 (2015) 98-119 eq. (25).
Marc-Antoine Coppo and Bernard Candelpergher, <a href="http://dx.doi.org/10.1016/j.jn.2014.11.007">Inverse binomial series and values of Arakawa-Kaneko zeta functions</a>, J. Number Theory 150 (2015) 98-119 eq. (25).
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G(1) = Pi^4/480 - (1/4)*Sum_{r>=2} (-1)^r*H(r-1,2)/r^2, where H(n,m) is the n-th harmonic number of order m.
R. Sitaramachandrarao, <a href="http://dx.doi.org/10.1016/0022-314X(87)90012-6">A Formula of S. Ramanujan </a>, JOURNAL OF NUMBER THEORY Journal of Number Theory 25, 1-19 (1987)