Certain new formulas for bibasic Humbert hypergeometric functions $\Psi_{1}$ and $\Psi_{2}$
Classical Analysis and ODEs
2022-07-06 v1
Abstract
The main aim of the present work is to give some interesting the -analogues of various -recurrence relations, -recursion formulas, -partial derivative relations, -integral representations, transformation and summation formulas for bibasic Humbert hypergeometric functions and on two independent bases and of two variables and some developments formulae, believed to be new, by using the conception of -calculus. Finally, some interesting special cases and straightforward identities connected with bibasic Humbert hypergeometric series of the types and are established when the two independent bases and are equal.
Keywords
Cite
@article{arxiv.2207.01689,
title = {Certain new formulas for bibasic Humbert hypergeometric functions $\Psi_{1}$ and $\Psi_{2}$},
author = {Ayman Shehata},
journal= {arXiv preprint arXiv:2207.01689},
year = {2022}
}