Dual q-Krawtchouk polynomials

In mathematics, the dual q-Krawtchouk 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 by

Orthogonality

Recurrence and difference relations

Rodrigues formula

Generating function

Relation to other polynomials
gollark: ```haskellimport Unsafe.Coerceimport System.IO.Unsafedata OS = CCIsBad String deriving Showdata The = The deriving Showdata Best = The OS deriving Showdata PotatOS = Is The Best OS deriving ShowpotatOS = unsafePerformIO . unsafeInterleaveIO . unsafeCoerce; potatOS :: () -> PotatOS```
gollark: What about `^`, `*`, `*`, unary `-`, `%` etc?
gollark: Ah, you want arrow operators.
gollark: So this, but without passing the result of one to the other...?
gollark: You mean, combine their bytecode or something insane?

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
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