Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Bibasic Humbert hypergeometric function $Φ_1$

Ayed Aledamat, Ayman Shehata

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 $Φ_1$ 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.

On Bibasic Humbert hypergeometric function $Φ_1$

Abstract

The main aim of this work is to derive the -recurrence relations, -partial derivative relations and summation formula of bibasic Humbert hypergeometric function on two independent bases and of two variables and some developments formulae, believed to be new, by using the conception of -calculus.
Paper Structure (3 sections, 7 theorems, 38 equations)

This paper contains 3 sections, 7 theorems, 38 equations.

Table of Contents

  1. Introduction
  2. Main Results
  3. Concluding remarks

Key Result

Theorem 2.1

The following relations for $\Phi_{1}$ are true and

Theorems & Definitions (14)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • proof
  • Theorem 2.4
  • proof
  • Theorem 2.5
  • proof
  • ...and 4 more