Quadratic Transformations of Hypergeometric Function and Series with Harmonic Numbers

Abstract

In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that contain one or two continuous parameters. We also give a generating function of the sequence $\frac{(a{)}_n(1-a{)}_n}{(n!{)}^2}{H}_n$ as a combination of Gauss hypergeometric function and elementary functions.

arXiv comment8 pages. Corollary 3 is added

References in corpus (3)

• On a three-dimensional symmetric Ising tetrahedron, and contributions to the theory of the dilogarithm and Clausen functions
• The integrals in Gradshteyn and Ryzhik. Part 16: Complete elliptic integrals
• Watson-type 3F2-series and summation formulae involving generalized harmonic numbers

Cited by in corpus (1)

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