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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2023, Volume 8, Issue 4, Pages 553–567
DOI: https://doi.org/10.47475/2500-0101-2023-8-4-553-567 (Mi chfmj349) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Multiple Euler integral representations for the Kampé de Fériet functions

T. G. Ergasheva, A. Hasanovbc, T. K. Yuldashevd

a National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, Tashkent, Uzbekistan
b Romanovskiy Institute of Mathematics, National Academy of Sciences, Tashkent, Uzbekistan
c Ghent University, Ghent, Belgium
d Tashkent State University of Economics, Tashkent, Uzbekistan
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DOI: https://doi.org/10.47475/2500-0101-2023-8-4-553-567
Abstract: By the aid of Appell, Humbert and Bessel functions, the integral representations for a Kampé de Fériet function are found. The validity of integral representations for a Kampé de Fériet function of general form are proved. Conditions, under which these representations are expressed in terms of products of two generalized hypergeometric functions are found. Examples, in which the integral representation of the Kampé de Fériet function containing Appell, Humbert or Bessel functions, are identified.
Keywords: Kampé de Fériet functions, multiple Euler type integral representations, generalized hypergeometric functions of second order, Bessel function, Appell functions, Humbert functions.
Funding agency Grant number
Ghent University G.0H94.18N
01M01021
The research is supported by the Intercontinental Research Center “Analysis and PDE” (Ghent University, Belgium), grant G.0H94.18N and by the Special Research Fund of Methusalem programme (Ghent University), grant 01M01021.
Received: 08.08.2023
Revised: 21.09.2023
Document Type: Article
UDC: 517.552
Language: English
Citation: T. G. Ergashev, A. Hasanov, T. K. Yuldashev, “Multiple Euler integral representations for the Kampé de Fériet functions”, Chelyab. Fiz.-Mat. Zh., 8:4 (2023), 553–567
Citation in format AMSBIB
\Bibitem{ErgHasYul23}
\by T.~G.~Ergashev, A.~Hasanov, T.~K.~Yuldashev
\paper Multiple Euler integral representations for the Kamp\'e de F\'eriet functions
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2023
\vol 8
\issue 4
\pages 553--567
\mathnet{http://mi.mathnet.ru/chfmj349}
\crossref{https://doi.org/10.47475/2500-0101-2023-8-4-553-567}
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