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On the q-Hypergeometric Matrix Function _{r}φ_{s}(A, B; C_{i}; D_{j}; q; z) and Its q-Fractional Calculus

## DOI:

https://doi.org/10.18311/jims/2024/36132## Keywords:

Basic hypergeometric function, Mittag-Leffer function, Matrix functional calculus.## Abstract

In this paper, we introduce a q-hypergeometric matrix function _{r}φ_{s}(A, B; C_{i}; D_{j}; q; z) and investigate their regions of convergence. We determine some q-matrix contiguous function relations, a q-integral representation and q-difference formulas satisfied by _{r}φ_{s}(A, B; C_{i}; D_{j}; q; z) Certain properties of this matrix function have also been studied from q-fractional calculus point of view. Finally, we emphasize on the special cases of _{r}φ_{s}(A, B; C_{i}; D_{j}; q; z).

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## How to Cite

*The Journal of the Indian Mathematical Society*,

*91*(1-2), 11–24. https://doi.org/10.18311/jims/2024/36132

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Copyright (c) 2024 Ravi Dwivedi, Reshma Sanjhira

This work is licensed under a Creative Commons Attribution 4.0 International License.

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