Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the discrete analogues of Appell function $F_3$

Ravi Dwivedi, Vivek Sahai

Abstract

The present paper is devoted to the study of Appell hypergeometric function $F_3$ from discrete point of view. We mainly introduce two generalized discrete forms of $F_3$ and study their basic properties \emph{viz.} regions of convergence, difference-differential equations, integral representations, finite and infinite sums, recursion formulae, to name a few.

On the discrete analogues of Appell function $F_3$

Abstract

The present paper is devoted to the study of Appell hypergeometric function from discrete point of view. We mainly introduce two generalized discrete forms of and study their basic properties \emph{viz.} regions of convergence, difference-differential equations, integral representations, finite and infinite sums, recursion formulae, to name a few.
Paper Structure (13 sections, 7 theorems, 60 equations)

This paper contains 13 sections, 7 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. The discrete Appell function $\mathcal{F}_3^{(1)}$
  3. Difference equations
  4. Integral representations
  5. Differential and difference formulae
  6. Finite and infinite sum
  7. Recursion Formulae
  8. The discrete Appell function $\mathcal{F}_3^{(2)}$
  9. Integral representations
  10. Differential formulae
  11. Finite and infinite sums
  12. Recursion Formulae
  13. Conclusion

Key Result

Theorem 2.1

The discrete Appell function $\mathcal{F}^{(1)}_3$ satisfy the following difference equations:

Theorems & Definitions (12)

  • Theorem 2.1
  • proof
  • Theorem 2.2
  • proof
  • Theorem 3.1
  • proof
  • Theorem 4.1
  • proof
  • Theorem 5.1
  • proof
  • ...and 2 more