Weights whose biorthogonal polynomials admit a Rodrigues formula

[摘要] Let alpha > 0 and psi(x) = x(alpha). Let to be a non-negative integrable function on an interval I. Let P-n be a polynomial of degree n determined by the biorthogonality conditions integral(I) P-n psi(j)w=0, j=0,1,...,n-1. We determine for which weights w, P-n admits an analogue of the classical Rodrigues formula for orthogonal polynomials, and present the formula whenever it exists. We also provide generating functions and fairly explicit representations for P-n. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] orthogonal polynomials;biorthogonal polynomials;Rodrigues formula;Jacobi;Laguerre;hermite weights;Sidi polynomials