# Article ID: MTJPAM-D-21-00019

## Title: Decomposition Formulas for Second-Order Quadruple Gaussian Hypergeometric Series by Means of Operators H(α,β) and H(α,β)

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00019; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 41-60

Document Type: Research Paper

Author(s): Anvar Hasanov a , Ainur Ryskan b , Junesang Choi c

aInstitute of Mathematics, Uzbek Academy of Sciences, 81 Mirzo-Ulugbek street, Tashkent 700170, Uzbekistan

bNational Pedagogical University, 86 Tole bi street, Almaty 0500012, Kazakhstan

cDepartment of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea

Received: 2 February 2021, Accepted: 15 July 2021, Published: 30 July 2021.

Corresponding Author: Junesang Choi (Email address: junesang@dongguk.ac.kr)

Full Text: PDF

Abstract

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.

Keywords: Hypergeometric functions, Multiple hypergeometric functions, Inverse pairs of symbolic operators, Decomposition formulas, Mellin-Barnes contour integrals

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