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

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

February 20, 1996 | Roelof Koekoek, René F. Swarttouw
The paper presents the Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. It lists all classes of orthogonal polynomials in the Askey-scheme, including their definitions, orthogonality relations, three-term recurrence relations, and generating functions. It also describes the limit relations between different classes of orthogonal polynomials in the scheme. The q-analogue of the Askey-scheme is also discussed, including the definitions, orthogonality relations, three-term recurrence relations, and generating functions of the q-analogues of the polynomials in the scheme. The paper also explains how the classical hypergeometric orthogonal polynomials can be obtained from their q-analogues. The authors thank Professor Tom H. Koornwinder for his guidance and support. The paper includes a detailed list of all the orthogonal polynomials in the Askey-scheme and their q-analogues, along with their limit relations. The authors also mention that they plan to add recurrence relations for monic polynomials and include more formulas with quadratic transformations in future versions of the report. The paper is a comprehensive reference for the theory of hypergeometric orthogonal polynomials and their q-analogues.The paper presents the Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue. It lists all classes of orthogonal polynomials in the Askey-scheme, including their definitions, orthogonality relations, three-term recurrence relations, and generating functions. It also describes the limit relations between different classes of orthogonal polynomials in the scheme. The q-analogue of the Askey-scheme is also discussed, including the definitions, orthogonality relations, three-term recurrence relations, and generating functions of the q-analogues of the polynomials in the scheme. The paper also explains how the classical hypergeometric orthogonal polynomials can be obtained from their q-analogues. The authors thank Professor Tom H. Koornwinder for his guidance and support. The paper includes a detailed list of all the orthogonal polynomials in the Askey-scheme and their q-analogues, along with their limit relations. The authors also mention that they plan to add recurrence relations for monic polynomials and include more formulas with quadratic transformations in future versions of the report. The paper is a comprehensive reference for the theory of hypergeometric orthogonal polynomials and their q-analogues.
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