q-Meixner polynomials
In mathematics, the q-Meixner polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.
Definition
The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol.
Orthogonality
Recurrence and difference relations
Rodrigues formula
Generating function
Relation to other polynomials
gollark: https://en.wikipedia.org/wiki/Hard_disk_drive_platter
gollark: With some sort of weird coatings.
gollark: Apparently, aluminium or glass/ceramic.
gollark: Plus probably some more for overheads.
gollark: Ah, but if you want to just destroy the Earth by splitting it into unreasonably small pieces, you just need enough antimatter to overcome the gravitational binding energy.
References
- Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, 96 (2nd ed.), Cambridge University Press, doi:10.2277/0521833574, ISBN 978-0-521-83357-8, MR 2128719
- Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010), Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, doi:10.1007/978-3-642-05014-5, ISBN 978-3-642-05013-8, MR 2656096
- Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F. (2010), http://dlmf.nist.gov/18
|contribution-url=missing title (help), 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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.