Abstract
The main object of this paper is to deduce the bibasic Humbert functions Ξ1 and Ξ2 Some interesting results and elementary summations technique that was successfully employed, q–recursion, q–derivatives relations, the q–differential recursion relations, the q–integral representations for Ξ1 and Ξ2 are given. The summation formula derives a list of p–analogues of transformation formulas for bibasic Humbert functions that have been studied, also some hypergeometric functions properties of some new interesting special cases have been given.
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The authors are very grateful to the anonymous referees for many valuable comments and suggestions which helped to improve the paper.
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Supported by the National Natural Science Foundation of China(11601266) and the Natural Science Foundation of Fujian Province of China(2020J01783).
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Cai, Qb., Khammash, G.S., Moustafa, S.I. et al. On some properties of the bibasic Humbert hypergeometric functions Ξ1 and Ξ2. Appl. Math. J. Chin. Univ. 38, 614–630 (2023). https://doi.org/10.1007/s11766-023-4848-8
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DOI: https://doi.org/10.1007/s11766-023-4848-8