Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials
Volume 29 / 2002
Applicationes Mathematicae 29 (2002), 97-116
MSC: 33C45, 42A16, 42C10, 42C15, 65Q05.
DOI: 10.4064/am29-1-9
Abstract
Let $\{ P_k\} $ be any sequence of classical orthogonal polynomials. Further, let $f$ be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfied by the coefficients $a_k$ in $f=\sum _{k}a_kP_k$. A systematic use of the basic properties (including some nonstandard ones) of the polynomials $\{ P_k\} $ results in obtaining a low order of the recurrence.
