Malaysian Journal of Mathematical Sciences, March 2023, Vol. 17, No. 1

On Bibasic Humbert Hypergeometric Function $\Phi_{1}$

AL E'damat, A. and Shehata, A.

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Received date: 30 July 2022
Accepted date: 18 September 2022

The main aim of this work is to derive the $q$-recurrence relations, $q$-partial derivative relations and summation formula of bibasic Humbert hypergeometric function $\Phi_{1}$ on two independent bases $q$ and $q_{1}$ of two variables and some developments formulae, believed to be new, by using the conception of $q$-calculus.

Keywords: $q$-calculus; bibasic Humbert hypergeometric functions; $q$-derivative



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