Geodesic
Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials
Stanislaw Lewanowicz1
1 Institute of Computer Science University of Wrocław Przesmyckiego 20 51-151 Wrocław, Poland
Applicationes Mathematicae, Tome 29 (2002) no. 1, pp. 97-116.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am29-1-9
Keywords: sequence classical orthogonal polynomials further function satisfying linear differential equation polynomial coefficients algorithm construct compact form recurrence relation satisfied coefficients sum systematic basic properties including nonstandard polynomials results obtaining low order recurrence

Stanislaw Lewanowicz 1

1 Institute of Computer Science University of Wrocław Przesmyckiego 20 51-151 Wrocław, Poland 
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Stanislaw Lewanowicz. Recurrences for the coefficients of series
  expansions with respect to classical
  orthogonal polynomials. Applicationes Mathematicae, Tome 29 (2002) no. 1, pp. 97-116. doi : 10.4064/am29-1-9. http://geodesic.mathdoc.fr/articles/10.4064/am29-1-9/

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