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

Stanislaw Lewanowicz. "Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials." Applicationes Mathematicae 29.1 (2002): 97-116. <http://eudml.org/doc/278966>.

@article{StanislawLewanowicz2002,
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 $f = ∑_\{k\}a_kP_k$. 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.},
author = {Stanislaw Lewanowicz},
journal = {Applicationes Mathematicae},
keywords = {classical orthogonal polynomials; Fourier coefficients; recurrences},
language = {eng},
number = {1},
pages = {97-116},
title = {Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials},
url = {http://eudml.org/doc/278966},
volume = {29},
year = {2002},
}

TY - JOUR
AU - Stanislaw Lewanowicz
TI - Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials
JO - Applicationes Mathematicae
PY - 2002
VL - 29
IS - 1
SP - 97
EP - 116
AB - 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 $f = ∑_{k}a_kP_k$. 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.
LA - eng
KW - classical orthogonal polynomials; Fourier coefficients; recurrences
UR - http://eudml.org/doc/278966
ER -