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Algebra i Analiz, 1994, Volume 6, Issue 3, Pages 161–184 (Mi aa457)  
This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Gauss hypergeometric function and quadratic $R$-matrix algebras

T. H. Koornwinder, V. B. Kuznetsov

University of Amsterdam
Full-text PDF (2252 kB) Citations (9)
Abstract: We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with W. Miller's treatment of Lie algebras of first order differential operators will be discussed.
Keywords: Quadratic $R$-matrix algebras, Gauss hypergeometric function, classical orthogonal polynomials, recurrence relations.
Received: 23.12.1993
Bibliographic databases:
Document Type: Article
Language: English
Citation: T. H. Koornwinder, V. B. Kuznetsov, “Gauss hypergeometric function and quadratic $R$-matrix algebras”, Algebra i Analiz, 6:3 (1994), 161–184; St. Petersburg Math. J., 6:3 (1995), 595–618
Citation in format AMSBIB
\Bibitem{KooKuz94}
\by T.~H.~Koornwinder, V.~B.~Kuznetsov
\paper Gauss hypergeometric function and quadratic $R$-matrix algebras
\jour Algebra i Analiz
\yr 1994
\vol 6
\issue 3
\pages 161--184
\mathnet{http://mi.mathnet.ru/aa457}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1301836}
\zmath{https://zbmath.org/?q=an:0841.33002}
\transl
\jour St. Petersburg Math. J.
\yr 1995
\vol 6
\issue 3
\pages 595--618
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
     
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