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Abstract

In this contribution we analyze the generating functions for polynomials orthogonal with respect to a symmetric linear functional u, i.e., a linear application in the linear space of polynomials with complex coefficients such that u(x 2n+1 ) = 0. In some cases we can deduce explicitly the expression for the generating functionwhere {Pn}n is the sequence of orthogonal polynomials with respect to u.

A Classification of Symmetric (1, 1)-Coherent Pairs of Linear Functionals

“…Semiclassical symmetric linear functionals of order at most two are the natural framework of our study. They have been analyzed by many authors (see [33][34][35][36][37], among others). On the other hand, the so-called symmetrization process for linear functionals (see [3]) will play a central role in this contribution.…”