On series, integrals and continued fractions. III (Q2759131)

This is the third of several articles on closed form formulas for infinite series of the type \(\sum_{n=1}^\infty f(n) H_n^k\), where \(H_n\) is the \(n\)th partial sum of the harmonic series, and \(f(n)\) tends to 0 fast enough to ensure convergence of the series under consideration. The methods are elementary, using polynomial identities and partial summation. NEWLINENEWLINENEWLINEFor Parts I and II, cf. the author, Hardy-Ramanujan J. 4, Suppl., 1-11 (1981; Zbl 0464.33002), the author and \textit{R. Sitaramachandrarao}, Madras Univ. J., Sect. B 51, 181-198 (1988).