Some observations on derivatives of orthogonal polynomials

Abstract

In this paper it is shown that if {Ø_n(x)} is a set of orthogonal polynomials with the weight function w(x) in the finite interval (a, b), and if we assume that the derivatives {Ø'_n(x)} also form a set of orthogonal polynomials in a certain interval (c, d) (finite or infinite), with a non-negative weight function q (x), where (c,d) ≡ (a,b), then {Ø_n(x)} is a set of Jacobi polynomials.

Keywords: Polynomials, Weight Function, Derivative