On series, integrals and continued fractions. III (Q2759131)
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scientific article; zbMATH DE number 1680964
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On series, integrals and continued fractions. III |
scientific article; zbMATH DE number 1680964 |
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11 December 2001
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closed form formulas
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infinite series
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harmonic series
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polynomial identities
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partial summation
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On series, integrals and continued fractions. III (English)
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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).
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