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

• Autorzy: Stanislaw Lewanowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42C15: General harmonic expansions, frames
• 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
• 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2002
• Tom: 29
• Numer: 1
• Strony: 97-116

Daty

wydano

2002

Twórcy

autor

Stanislaw Lewanowicz

• Institute of Computer Science, University of Wrocław, Przesmyckiego 20, 51-151 Wrocław, Poland

Identyfikatory

DOI

10.4064/am29-1-9