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Ratios of the Gauss Hypergeometric Functions with Parameters Shifted by Integers: More on Integral Representations

Authors
  • Dyachenko, A.1
  • Karp, D.2
  • 1 Keldysh Institute of Applied Mathematics (RAS), Moscow, 125047, Russia , Moscow (Russia)
  • 2 School of Economics and Management and Far Eastern Center for Research and Education in Mathematics, Far Eastern Federal University, Vladivostok, 690922, Russia , Vladivostok (Russia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Dec 13, 2021
Volume
42
Issue
12
Pages
2764–2776
Identifiers
DOI: 10.1134/S1995080221120118
Source
Springer Nature
Keywords
Disciplines
  • Article
License
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Abstract

AbstractWe consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for this ratio based on a formula for its imaginary part. This work extends our recent results by lifting certain restrictions on parameters. The new representations are illustrated with a few examples and an application to products of ratios.

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