Mathematics

Expansions of Kampé de Fériet hypergeometric functions

N. J. Komilova^a, T. G. Ergashev^b, A. Hasanov<sup>c

a</sup> Fergana State University, Fergana, Uzbekistan
^b National Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”, Tashkent, Uzbekistan
^c V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan

Abstract: In 1940–1941, Burchnall and Chaundy, using the inverse pairs of symbolic operators introduced, systematically presented a number of expansion formulas for second-order Appell and Humbert hypergeometric functions in series of simpler hypergeometric functions. In 2006, Hasanov and Srivastava generalized Burchnall–Chaundy operators and found expansions for a class of multiple hypergeometric functions, however, the application of these operators is still limited to second-order hypergeometric functions. In this paper, we obtain expansions for the Kampé de Fériet functions of arbitrary orders.

Keywords: Appell functions, Humbert functions, Burchnall–Chaundy operators, Kampé de Fériet functions, expansions of hypergeometric functions.

UDC: 517.55

Received: 27.12.2023
Revised: 31.01.2025

Language: English

DOI: 10.47475/2500-0101-2025-10-3-513-526