Publication: Connection coefficients for Laguerre-Sobolev orthogonal polynomials
Loading...
Identifiers
Publication date
2003-07-15
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Export
Abstract
^aLaguerre–Sobolev polynomials are orthogonal with respect to an inner product of the form $$\langle p,q\rangle=\int_0^{\infty}p(x)q(x)x^{\alpha}e^{-x}\,dx +\lambda\int_0^{\infty}p'(x)q'(x)\,d\mu(x),$$ with $\alpha>-1,\ \lambda>0$, and p,q in P, the linear space of polynomials with real coefficients.
For each of these two families of Laguerre–Sobolev polynomials [see attached full-text paper], here we give the explicit expression of the connection coefficients in their expansion as a series of standard Laguerre polynomials. The inverse connection problem of expanding Laguerre polynomials in series of Laguerre–Sobolev polynomials, and the connection problem relating two families of Laguerre–Sobolev polynomials with different parameters, are also considered.
For each of these two families of Laguerre–Sobolev polynomials [see attached full-text paper], here we give the explicit expression of the connection coefficients in their expansion as a series of standard Laguerre polynomials. The inverse connection problem of expanding Laguerre polynomials in series of Laguerre–Sobolev polynomials, and the connection problem relating two families of Laguerre–Sobolev polynomials with different parameters, are also considered.
Description
19 pages, no figures.-- MSC2000 codes: 33C45, 42C05.
MR#: MR1991819 (2004h:33020)
Zbl#: Zbl 1033.42027
MR#: MR1991819 (2004h:33020)
Zbl#: Zbl 1033.42027
Keywords
Laguerre polynomials, Sobolev inner products, Connection coefficients
Bibliographic citation
Journal of Mathematical Analysis and Applications, 2003, vol. 283, n. 2, p. 440-458