Representations of orthogonal polynomials (Q1392783)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Representations of orthogonal polynomials |
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Representations of orthogonal polynomials (English)
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18 February 1999
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The paper gives extensions of earlier results of the authors by presenting a collection of algorithms with which any of the conversions between the differential/difference equation, the hypergeometric representation, and the recurrence equation of a given orthogonal polynomial is possible. An algorithm for computing recurrence relations for connection coefficients is given. Zeilberger's algorithm and further versions of this algorithm are important tools in this work.
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Jacobi polynomials
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Gegenbauer polynomials
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Bessel polynomials
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Laguerre polynomials
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Hermite polynomials
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Hahn polynomials
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Krawchouk polynomials
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Meixner polynomials
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Charlier polynomials
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Zeilberger's algorithm
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Petkovšek's algorithm
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recurrence relations
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hypergeometric function
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