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arXiv · 2610.34066

On transformations of Kampé de Fériet functions with integral parameter differences

Kirill Bakhtin
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Abstract

We obtain analogues of the first Miller--Paris transformation for three classes of Kampé de Fériet functions with unit parameter differences associated with the Appell function $F_1$. We also derive representations of the Appell function $F_1$ in terms of Kampé de Fériet functions and reduction formulas expressing certain Kampé de Fériet functions with integral parameter differences in terms of univariate generalized hypergeometric functions with integral parameter differences.

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Kirill Bakhtin. 2026-10-25. On transformations of Kampé de Fériet functions with integral parameter differences. https://arxiv.org/abs/2610.34066

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