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Mosc. Math. J., 2015, Volume 15, Number 2, Pages 293–318 (Mi mmj560)  

This article is cited in 1 scientific paper (total in 1 paper)

Some transformation formulas associated with Askey–Wilson polynomials and Lassalle's formulas for Macdonald–Koornwinder polynomials

A. Hoshinoa, M. Noumib, J. Shiraishic

a Kagawa National College of Technology, 355 Chokushi-cho, Takamatsu, Kagawa 761-8058, Japan
b Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
c Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan

Abstract: We present a fourfold series expansion representing the Askey–Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's $q$-extension of the Field and Wimp expansion, Andrews' terminating $q$-analogue of Watson's $_3F_2$ sum, Singh's quadratic transformation. As an application, we present an explicit formula for the Koornwinder polynomial of type $BC_n$ ($n\in\mathbb Z_{>0}$) with one row diagram. When the parameters are specialized, we recover Lassalle's formula for Macdonald polynomials of type $B_n$, $C_n$ and $D_n$ with one row diagram, thereby proving his conjectures.

Key words and phrases: Askey–Wilson polynomial.

DOI: https://doi.org/10.17323/1609-4514-2015-15-2-293-318

Full text: http://www.mathjournals.org/.../2015-015-002-007.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 33D45, 33D52
Received: June 6, 2014; in revised form December 27, 2014
Language:

Citation: A. Hoshino, M. Noumi, J. Shiraishi, “Some transformation formulas associated with Askey–Wilson polynomials and Lassalle's formulas for Macdonald–Koornwinder polynomials”, Mosc. Math. J., 15:2 (2015), 293–318

Citation in format AMSBIB
\Bibitem{HosNouShi15}
\by A.~Hoshino, M.~Noumi, J.~Shiraishi
\paper Some transformation formulas associated with Askey--Wilson polynomials and Lassalle's formulas for Macdonald--Koornwinder polynomials
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 2
\pages 293--318
\mathnet{http://mi.mathnet.ru/mmj560}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-2-293-318}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427425}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361607300007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. Shiraishi, A. Hoshino, “Macdonald Polynomials of Type $\boldsymbol{C_n}$ with One-Column Diagrams and Deformed Catalan Numbers”, SIGMA, 14 (2018), 101, 33 pp.  mathnet  crossref
  • Moscow Mathematical Journal
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