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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 F1. We also derive representations of the Appell function F1 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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Cite

BibTeXRIS
BibTeX
@misc{bakhtin2026transformations,
  title = {{On transformations of Kampé de Fériet functions with integral parameter differences}},
  author = {Kirill Bakhtin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34066},
  eprint = {2610.34066},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34066},
}
RIS
TY  - UNPB
TI  - On transformations of Kampé de Fériet functions with integral parameter differences
AU  - Kirill Bakhtin
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34066
UR  - https://arxiv.org/abs/2610.34066
AB  - 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.
ER  -