Abstract
In this paper, by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011, we establish several decomposition formulas associated with the Gaussian triple hypergeometric functions. Some transformation formulas for these functions have also been obtained.
Highlights
The use of many mathematical operations goes beyond the class of elementary functions
Multiple hypergeometric functions occur in numerous problems in hydrodynamics, control theory, electrical current, heat conduction, and classical and quantum mechanics
Based on the operators (12) and (13), we aim in this work to establish certain decomposition formulas for second-order Gaussian hypergeometric functions in three variables (1), (2), (3), (4), (5), (6), (7), (8), (9), and (10), which are used to derive some interesting transformation formulas for these functions
Summary
The use of many mathematical operations goes beyond the class of elementary functions. The great success of the theory of hypergeometric functions in a single variable has stimulated the development of the theory of hypergeometric functions in several variables by the fact that the solutions of partial differential equations arising in many applied problems of mathematical physics are given in terms of such hypergeometric functions (see, e.g., [1,2,3,4,5,6]). Based on the operators (12) and (13), we aim in this work to establish certain decomposition formulas for second-order Gaussian hypergeometric functions in three variables (1), (2), (3), (4), (5), (6), (7), (8), (9), and (10), which are used to derive some interesting transformation formulas for these functions
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