Representations of orthogonal polynomials:
Abstract: "Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals. Further versions...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1997
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| Series: | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin
1997,6 |
| Subjects: | |
| Summary: | Abstract: "Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals. Further versions of this algorithm allow the computation of recurrence and differential equations from Rodrigues type formulas and from generating functions. In particular, these algorithms can be used to compute the differential/difference and recurrence equations for the classical continuous and discrete orthogonal polynomials from their hypergeometric representations, and from their Rodrigues representations and generating functions. In recent work, we used an explicit formula for the recurrence equation of families of classical continuous and discrete orthogonal polynomials, in terms of the coefficients of their differential/difference equations, to give an algorithm to identify the polynomial system from a given recurrence equation. In this article we extend these results be [sic] presenting a collection of algorithms with which any of the conversions between the differential/difference equation, the hypergeometric representation, and the recurrence equation is possible. The main technique is again to use explicit formulas for structural identities of the given polynomial systems." |
| Physical Description: | 33 S. |
Staff View
MARC
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| 100 | 1 | |a Koepf, Wolfram |d 1953- |e Verfasser |0 (DE-588)136291279 |4 aut | |
| 245 | 1 | 0 | |a Representations of orthogonal polynomials |c Wolfram Koepf ; Dieter Schmersau |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1997 | |
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| 490 | 1 | |a Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |v 1997,6 | |
| 520 | 3 | |a Abstract: "Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals. Further versions of this algorithm allow the computation of recurrence and differential equations from Rodrigues type formulas and from generating functions. In particular, these algorithms can be used to compute the differential/difference and recurrence equations for the classical continuous and discrete orthogonal polynomials from their hypergeometric representations, and from their Rodrigues representations and generating functions. In recent work, we used an explicit formula for the recurrence equation of families of classical continuous and discrete orthogonal polynomials, in terms of the coefficients of their differential/difference equations, to give an algorithm to identify the polynomial system from a given recurrence equation. In this article we extend these results be [sic] presenting a collection of algorithms with which any of the conversions between the differential/difference equation, the hypergeometric representation, and the recurrence equation is possible. The main technique is again to use explicit formulas for structural identities of the given polynomial systems." | |
| 650 | 4 | |a Hypergeometric series | |
| 650 | 4 | |a Orthogonal polynomials | |
| 700 | 1 | |a Schmersau, Dieter |d 1942- |e Verfasser |0 (DE-588)143446444 |4 aut | |
| 810 | 2 | |a Konrad-Zuse-Zentrum für Informationstechnik Berlin |t Preprint SC |v 1997,6 |w (DE-604)BV004801715 |9 1997,6 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010359914 | |
Record in the Search Index
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| author_facet | Koepf, Wolfram 1953- Schmersau, Dieter 1942- |
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| building | Verbundindex |
| bvnumber | BV017188908 |
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| discipline | Informatik |
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| id | DE-604.BV017188908 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:07:56Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010359914 |
| oclc_num | 37991502 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 33 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series2 | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| spelling | Koepf, Wolfram 1953- Verfasser (DE-588)136291279 aut Representations of orthogonal polynomials Wolfram Koepf ; Dieter Schmersau Berlin Konrad-Zuse-Zentrum für Informationstechnik 1997 33 S. txt rdacontent n rdamedia nc rdacarrier Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin 1997,6 Abstract: "Zeilberger's algorithm provides a method to compute recurrence and differential equations from given hypergeometric series representations, and an adaption of Almquist and Zeilberger computes recurrence and differential equations for hyperexponential integrals. Further versions of this algorithm allow the computation of recurrence and differential equations from Rodrigues type formulas and from generating functions. In particular, these algorithms can be used to compute the differential/difference and recurrence equations for the classical continuous and discrete orthogonal polynomials from their hypergeometric representations, and from their Rodrigues representations and generating functions. In recent work, we used an explicit formula for the recurrence equation of families of classical continuous and discrete orthogonal polynomials, in terms of the coefficients of their differential/difference equations, to give an algorithm to identify the polynomial system from a given recurrence equation. In this article we extend these results be [sic] presenting a collection of algorithms with which any of the conversions between the differential/difference equation, the hypergeometric representation, and the recurrence equation is possible. The main technique is again to use explicit formulas for structural identities of the given polynomial systems." Hypergeometric series Orthogonal polynomials Schmersau, Dieter 1942- Verfasser (DE-588)143446444 aut Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 1997,6 (DE-604)BV004801715 1997,6 |
| spellingShingle | Koepf, Wolfram 1953- Schmersau, Dieter 1942- Representations of orthogonal polynomials Hypergeometric series Orthogonal polynomials |
| title | Representations of orthogonal polynomials |
| title_auth | Representations of orthogonal polynomials |
| title_exact_search | Representations of orthogonal polynomials |
| title_full | Representations of orthogonal polynomials Wolfram Koepf ; Dieter Schmersau |
| title_fullStr | Representations of orthogonal polynomials Wolfram Koepf ; Dieter Schmersau |
| title_full_unstemmed | Representations of orthogonal polynomials Wolfram Koepf ; Dieter Schmersau |
| title_short | Representations of orthogonal polynomials |
| title_sort | representations of orthogonal polynomials |
| topic | Hypergeometric series Orthogonal polynomials |
| topic_facet | Hypergeometric series Orthogonal polynomials |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT koepfwolfram representationsoforthogonalpolynomials AT schmersaudieter representationsoforthogonalpolynomials |