Abstract
In the spirit of Hasanov, Srivastava, and Turaev (2006), we introduce new inverse operators together with a more general operator and find a summation formula for the last one. Based on these operators and the earlier known q-analogues of the Burchnall-Chaundy operators, we find 15 symbolic operator formulas. Then, 10 expansions for the q-analogues of Srivastava’s three triple hypergeometric functions in terms of ϕ34q-hypergeometric and q-Kampé de Fériet functions are derived. These expansions readily reduce to 10 new expansions for the three triple Srivastava hypergeometric functions in terms of F34 hypergeometric and Kampé de Fériet functions.
Highlights
The concept of decomposition formulas for multiple hypergeometric functions is well known from the articles by Hasanov et al [1] and Bin-Saad [2]
The proofs of the following 15 formulas are straightforward from the definitions
To obtain the 10 new expansions for the three triple Srivastava hypergeometric functions in terms of 4F3 hypergeometric and Kampede Feriet functions mentioned in the abstract, let all ∞ disappear and adapt the indices for Φ
Summary
The concept of decomposition formulas for multiple hypergeometric functions is well known from the articles by Hasanov et al [1] and Bin-Saad [2]. This paper follows the first one by using q-analogues of 15 symbolic operator formulas. We find 10 expansions for these triple q-hypergeometric functions. The proofs show a certain symmetry, which is explained in detail in the last section
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