EXPANSIONS OF KAMP´E DE F´ERIET HYPERGEOMETRIC FUNCTIONS
N. J. KomilovaFergana State UniversityTuhtasin ErgashevNational Research University “Tashkent Institute of Irrigation and Agricultural Mechanization Engineers”Anvar HasanovV.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan
Челябинский физико-математический журналjournal2025
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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 Kamp´e de F´eriet functions of arbitrary orders.
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