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arXiv · 1806.00208

Degenerate Miller-Paris transformations

Dmitrii B. Karp·Elena G. Prilepkina
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Abstract

Important new transformations for the generalized hypergeometric functions with integral parameter differences have been discovered some years ago by Miller and Paris and studied in detail in a series of papers by a number of authors. These transformations fail if the free bottom parameter is greater than a free top parameter by a small positive integer. In this paper we fill this gap in the theory of Miller-Paris transformations by computing the limit cases of these transformations in such previously prohibited situations. This leads to a number of new transformation and summation formulas including extensions of Karlsson-Minton theorem.

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Dmitrii B. Karp, Elena G. Prilepkina. 2018-06-01. Degenerate Miller-Paris transformations. https://arxiv.org/abs/1806.00208

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