Charlier polynomials
Appearance
(Redirected from Poisson–Charlier polynomial)
![]() | This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. (May 2024) |
In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier. They are given in terms of the generalized hypergeometric function by
where are generalized Laguerre polynomials. They satisfy the orthogonality relation
They form a Sheffer sequence related to the Poisson process, similar to how Hermite polynomials relate to the Brownian motion.
See also
- Wilson polynomials, a generalization of Charlier polynomials.
References
- C. V. L. Charlier (1905–1906) Über die Darstellung willkürlicher Funktionen, Ark. Mat. Astr. och Fysic 2, 20.
- Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), "Hahn Class: Definitions", in Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248.
- Szegő, Gabor (1939), Orthogonal Polynomials, Colloquium Publications – American Mathematical Society, ISBN 978-0-8218-1023-1, MR 0372517