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On the discrete analogues of Appell function $F_4$

Ravi Dwivedi, Vivek Sahai

Abstract

In this paper, we study the Appell function $F_4$ from discrete point of view. In particular, we obtain regions of convergence, difference-differential equations, finite and infinite summation formulas and a list of recursion relations satisfied by the discrete analogues of Appell function $F_4$.

On the discrete analogues of Appell function $F_4$

Abstract

In this paper, we study the Appell function from discrete point of view. In particular, we obtain regions of convergence, difference-differential equations, finite and infinite summation formulas and a list of recursion relations satisfied by the discrete analogues of Appell function .
Paper Structure (7 sections, 3 theorems, 44 equations)

This paper contains 7 sections, 3 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Discrete Appell function $\mathcal{F}^{(1)}_4$
  3. Differential and difference formulae
  4. Recursion Formulae
  5. Discrete Appell function $F_4^{(2)}$
  6. Differential and difference formulae
  7. Recursion Formulae

Key Result

Theorem 3.1

The following difference and differential formulas are satisfied by discrete Appell function $\mathcal{F}^{(1)}_4$, where $\theta = x \frac{\partial}{\partial x}, \phi = y \frac{\partial}{\partial y}$:

Theorems & Definitions (6)

  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Theorem 4.1
  • proof