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...eter Lesky, Rene Swattouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p 443, Springer</ref> :<math>\displaystyle P_n(x;c;q)={}_3\phi_2(q^{-n},q^{n+1},x;q,cq;q,q) </math>. ...

...[[Jackson–Bessel function]]s, the Jackson-[[Wolfgang Hahn|Hahn]]-Cigler ''q''-addition, the [[Jackson derivative]], and the [[Jackson integral]]. *Ernst, T. (2012). A Comprehensive Treatment of q-Calculus. Springer Science & Business Media. ...

In mathematics, the '''continuous ''q''-Legendre polynomials''' are a family of basic hypergeometric [[orthogona | title = Hypergeometric orthogonal polynomials and their ''q''-analogues ...

...ő|authorlink=Gábor Szegő|year=1926}}, who was inspired by the continuous ''q''-Hermite polynomials studied by [[Leonard James Rogers]]. They are given b :<math>h_n(x;q) = \sum_{k=0}^n\frac{(q;q)_n}{(q;q)_k(q;q)_{n-k}}x^k</math> ...

...course of his work on the [[Rogers–Ramanujan identities]]. They are ''q''-analogs of [[ultraspherical polynomials]], and are the [[Macdonald polynomials]] fo ...Rogers polynomials can be defined in terms of the [[q-Pochhammer symbol|''q''-Pochhammer symbol]] and the [[basic hypergeometric series]] by ...

...polynomials]] introduced by [[Richard Askey]] and [[James A. Wilson]] as [[q-analog]]s of the [[Wilson polynomials]].{{sfnp|Askey|Wilson|1985}} They inc p_n(x;a,b,c,d\mid q) := ...

...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...ter Lesky, Rene Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p514, Springer</ref>。 ...

{{DISPLAYTITLE:''q''-Charlier polynomials }} ...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...

...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser :<math>K_n(\lambda(x);c,N|q)={}_3\phi_2(q^{-n},q^{-x},cq^{x-N};q^{-N},0|q;q),\quad n=0,1,2,...,N,</math> ...

{{distinguish|q-Meixner–Pollaczek polynomials}} {{DISPLAYTITLE:''q''-Meixner polynomials }} ...

{{distinguish|q-Meixner polynomials}} {{DISPLAYTITLE:''q''-Meixner–Pollaczek polynomials }} ...

{{DISPLAYTITLE: Quantum ''q''-Krawtchouk polynomials}} ...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...

...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...nomials are given in terms of [[basic hypergeometric function]]s and the [[q-Pochhammer symbol]] by ...

...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...n]]s by <ref>Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p. 501, Springer, 2010</ref> ...

...also|continuous q-Hahn polynomials|dual q-Hahn polynomials|continuous dual q-Hahn polynomials}} {{DISPLAYTITLE: ''q''-Hahn polynomials}} ...

{{DISPLAYTITLE: Continuous ''q''-Hahn polynomials }} ...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...

{{DISPLAYTITLE: Continuous ''q''-Hermite polynomials}} ...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...

{{DISPLAYTITLE: ''q''-Laguerre polynomials}} ...e also|big q-Laguerre polynomials|continuous q-Laguerre polynomials|little q-Laguerre polynomials}} ...

{{DISPLAYTITLE: Dual ''q''-Hahn polynomials}} ...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...

{{DISPLAYTITLE:Little ''q''-Jacobi polynomials}}{{No footnotes|date=May 2022}} ...w | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | ser ...