Decomposition Formulas for Second-Order Quadruple Gaussian Hypergeometric Series by Means of Operators H (α, β) and H (α, β)
Hasanov A. Ryskan A. Choi J.
2022MTJPAM Turkey
Montes Taurus Journal of Pure and Applied Mathematics
2022#4Issue 341 - 60 pp.
Numerous decomposition formulas for various hypergeometric functions of several variables have been offered. In this paper, we aim to establish symbolic operator identities and decomposition formulas for second-order quadruple Gaussian hypergeometric series associated with Appell functions and Saran hypergeometric functions by mainly using mutually inverse symbolic operators H (α, β) and H (α, β), which were introduced in an earlier work. Mellin-Barnes type contour integrals are employed for proofs of the operator identities. Also we determine the regions of convergence of the 14 quadruple Gaussian hypergeometric series.
Decomposition formulas , Hypergeometric functions , Inverse pairs of symbolic operators , Mellin-Barnes contour integrals , Multiple hypergeometric functions
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Institute of Mathematics, Uzbek Academy of Sciences, 81 Mirzo-Ulugbek street, Tashkent, 700170, Uzbekistan
National Pedagogical University, 86 Tole bi street, Almaty, 0500012, Kazakhstan
Department of Mathematics, Dongguk University, Gyeongju, 38066, South Korea
Institute of Mathematics
National Pedagogical University
Department of Mathematics
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