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...cs, the '''continuous ''q''-Legendre polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]].{{harvtxt|Koekoek| | title = Hypergeometric orthogonal polynomials and their ''q''-analogues ...

...ril 1960) was an English clergyman and mathematician who worked on [[basic hypergeometric series]]. He introduced several [[q-analog|''q''-analogs]] such as the [[Ja *Gasper, G., Rahman, M.(2004). Basic Hypergeometric Series. Cambridge University Press. ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The polynomials are given in terms of [[basic hypergeometric function]]s by ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] ...q-Pochhammer symbol]] by <ref>Roelof Koekoek, Peter Lesky, Rene Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p514, Springer</ref>。 ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The polynomials are given in terms of [[basic hypergeometric function]]s by ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The polynomials are given in terms of [[basic hypergeometric function]]s and the [[q-Pochhammer symbol]] by ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] ...etric function]]s and the [[q-Pochhammer symbol]] by ：<ref>Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analoques, p&nbsp;460, Springer</ref> ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag The polynomials are given in terms of [[basic hypergeometric function]]s by ...

{{short description|Special function in mathematics}} ...le generalization of the [[Generalized hypergeometric function|generalized hypergeometric series]], introduced by [[Joseph Kampé de Fériet]]. ...

{{Short description|A family of basic hypergeometric orthogonal polynomials}} ...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] ...

{{Short description|Family of hypergeometric orthogonal polynomials}} ...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The polynomials are given in terms of the [[basic hypergeometric function]] by ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] ...ven in terms of [[basic hypergeometric function]]s by <ref>Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p. 501, Springer, 2010</ref> ...

...sses the square of a [[Gaussian hypergeometric series]] as a [[generalized hypergeometric series]]. It states In particular it gives conditions for a hypergeometric series to be positive. This can be used to prove ...

{{Short description|Contour integral involving a product of gamma functions}} ...=Barnes|year1=1908|year2=1910}}. They are closely related to [[generalized hypergeometric series]]. ...

...metric orthogonal polynomials. They are defined in terms of [[generalized hypergeometric function]]s by ...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] ...

...''P''_''n''(''x'';''a'',''b'',''c'';''q'') are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]].<ref>{{citation |l The polynomials are given in terms of [[basic hypergeometric function]]s by ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The polynomials are given in terms of [[basic hypergeometric function]]s and the [[q-Pochhammer symbol]] by <ref>Mesuma Atakishiyeva, Na ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The polynomials are given in terms of [[basic hypergeometric function]]s and the [[q-Pochhammer symbol]] by <ref name=Roelof>Roelof p433 ...

...| last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag] The ''q''-Laguerre polynomials are given in terms of [[basic hypergeometric function]]s and the [[q-Pochhammer symbol]] by ...