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In mathematics, the Askey scheme is a way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in Andrews & Askey (1985), the Askey scheme was first drawn by Labelle (1985) and by Askey and Wilson (1985), and has since been extended by Koekoek & Swarttouw (1998) and Koekoek, Lesky & Swarttouw (2010) to cover basic orthogonal polynomials.
In mathematics, the Al-Salam–Chihara polynomialsQn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al-Salam and Chihara (1976). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14.8) give a detailed list of the properties of Al-Salam–Chihara polynomials.
In mathematics, Al-Salam–Carlitz polynomialsU(a)
n(x;q) and V(a)
n(x;q) are two families of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Waleed Al-Salam and Leonard Carlitz (1965). Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14.24, 14.25) give a detailed list of their properties.
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n(x;k) and Bλ
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In mathematics, sieved Jacobi polynomials are a family of sieved orthogonal polynomials, introduced by Askey (1984). Their recurrence relations are a modified version of the recurrence relations for Jacobi polynomials.
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References
- Al-Salam, Waleed; Allaway, W. R.; Askey, Richard (1984), "Sieved ultraspherical polynomials", Transactions of the American Mathematical Society , 284 (1): 39–55, CiteSeerX 10.1.1.308.3668 , doi:10.2307/1999273, ISSN 0002-9947, JSTOR 1999273, MR 0742411
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