Discrete Hypergeometric Legendre Polynomials

Abstract

A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials. We derive their difference equations, recurrence relations, and generating function.

Keywords

• Legendre polynomial
• hypergeometric function
• special functions
• recurrence relation
• generating function
• difference equation