Orthogonal Polynomials With Weight Function (1 - x)α( l + x)β + Mδ(x + 1) + Nδ(x - 1)

Abstract

AbstractWe study orthogonal polynomials for which the weight function is a linear combination of the Jacobi weight function and two delta functions at 1 and — 1. These polynomials can be expressed as 4F3 hypergeometric functions and they satisfy second order differential equations. They include Krall’s Jacobi type polynomials as special cases. The fourth order differential equation for the latter polynomials is derived in a more simple way.