Skip to main content

An extension of basic Humbert hypergeometric functions Φ1 , Φ2 and Φ3

Research Abstract

Given the growing quantity of proposals and works of basic hypergeometric functions in the
scope of q-calculus, it is important to introduce a systematic classification of q-calculus. Our aim in this article is to investigate several interesting q-partial derivative formulas, q-contiguous function relations, q-recurrence relations, various q-partial differential equations, summation formulas, transformation formulas and q-integrals representations for basic Humbert hypergeometric functions Φ1, Φ2 and Φ3 under constraints of symmetry parameters. These interesting properties, as special cases, include many known expansions of
basic Humbert hypergeometric functions Φ1, Φ2 and Φ3, and are also include particular interest in the area.

Research Authors
Ayman Shehata
Research Date
Research Department
Research Journal
Boletim da Sociedade Paranaense de Matemática
Research Pages
1-16
Research Publisher
SPM: www.spm.uem.br/bspm
Research Vol
44
Research Website
doi:10.5269/bspm.76663
Research Year
2026