Bilateral generating functions for a new class of generalized Legendre polynominals

Abstract

Recently Chatterjea (1) has proved a theorem to deduce a bilateral generating function for the Ultraspherical polynomials. In the present paper an attempt has been made to give a general version of Chatterjea's theorem. Finally, the theorem has been specialized to obtain a bilateral generating function for a class of polynomials {Pn(x;α,β)} introduced by Bhattacharjya (2).

Keywords

• bilateral generating function
• ultraspherical polynomials
• Legendre polynomials
• orthogonal polynomials
• weight function
• Rodrigue's formula.