English

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 qq-analogues of various qq-recurrence relations, qq-recursion formulas, qq-partial derivative relations, qq-integral representations, transformation and summation formulas for bibasic Humbert hypergeometric functions Ψ1\Psi_{1} and Ψ2\Psi_{2} on two independent bases qq and pp of two variables and some developments formulae, believed to be new, by using the conception of qq-calculus. Finally, some interesting special cases and straightforward identities connected with bibasic Humbert hypergeometric series of the types Ψ1\Psi_{1} and Ψ2\Psi_{2} are established when the two independent bases qq and pp 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}
}