On Bibasic Humbert hypergeometric function $Φ_1$ (2202.12697v3)

Abstract: 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.