Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials

Stanislaw Lewanowicz

Applicationes Mathematicae, Tome 29 (2002), p. 97-116 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $f = \sum_{k} a_{k} P_{k}$ . 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.

Publié le : 2002-01-01

Zbl 1008.33003

EUDML-ID : urn:eudml:doc:278966

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-9,
     author = {Stanislaw Lewanowicz},
     title = {Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials},
     journal = {Applicationes Mathematicae},
     volume = {29},
     year = {2002},
     pages = {97-116},
     zbl = {1008.33003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-9}
}

Stanislaw Lewanowicz. Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials. Applicationes Mathematicae, Tome 29 (2002) pp. 97-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-1-9/