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The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

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arxiv math/9602214 v1 pith:IXFMUISU submitted 1996-02-20 math.CA

Roelof Koekoek , René F. Swarttouw This is my paper · ORCID
classification math.CA
keywords polynomialsorthogonalaskey-schemerelationchaptergivehypergeometricclasses
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We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.

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