Beyond the beta integral method: transformation formulas for hypergeometric functions via Meijer's G function

Abstract

The beta integral method proved itself as a simple nonetheless powerful method of generating hypergeometric identities at a fixed argument. In this paper we propose a generalization by substituting the beta density with a particular type of Meijer's G function. By application of our method to known transformation formulas we derive about forty hypergeometric identities, majority of which are believed to be new. We further apply some of these transformations to obtain several new summation formulas.

arXiv commentSeveral summation formulas and concluding remarks added; References updated; number of typos corrected. precise copy of the published version; 33 pages; no figures

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• On hypergeometric functions and Pochhammer $k$-symbol
• Hypergeometric Differential Equation and New Identities for the Coefficients of Nørlund and Bühring
• Extensions of the Classical Transformations of 3F2
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Cited by in corpus (1)

• Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities