Some generating functions and properties of extended second Appell function

Abstract

Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing (presumably new) a generating function for the extended second Appell hypergeometric function $F_{2} (a, b, b'; c, c'; x, y; p)$. Further we derive a relation in terms of the Laguerre polynomials and differentiation formulas. We also present special cases of the main results of this paper.

Keywords

• Extended Beta function
• Extended hypergeometric function
• Generating functions
• Second Appell function
• Extended Second Appell function
• Laguerre polynomials