Multivariable big and little q-Jacobi polynomials

被引：15
|
作者：
Stokman, JV
机构：
[1] Faculty WINS, University of Amsterdam, 1018 TV Amsterdam
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1997年 / 28卷 / 02期
关键词：
big q-Jacobi polynomials; little q-Jacobi polynomials; BCn-type Askey-Wilson polynomials; multivariable orthogonal polynomials; q-extensions of Selberg's multidimensional beta-integrals;
D O I：
10.1137/S0036141095287192
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A four-parameter family of multivariable big q-Jacobi polynomials and a three-parameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality is proved with the help of a second-order q-difference operator which is diagonalized by the multivariable polynomials. A link is made between the orthogonality measures and R. Askey's q-extensions of Seiberg's multidimensional beta-integrals.
引用
收藏
页码：452 / 480
页数：29
相关论文
共 50 条
  • [1] On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials
    Atakishiyev, NM
    Klimyk, AU
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 294 (01) : 246 - 257
  • [2] Little and big q-Jacobi polynomials and the Askey–Wilson algebra
    Pascal Baseilhac
    Xavier Martin
    Luc Vinet
    Alexei Zhedanov
    [J]. The Ramanujan Journal, 2020, 51 : 629 - 648
  • [3] Multiple little q-Jacobi polynomials
    Postelmans, K
    Van Assche, W
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 178 (1-2) : 361 - 375
  • [4] Multiple big q-Jacobi polynomials
    Bouzeffour, Fethi
    Garayev, Mubariz
    [J]. BULLETIN OF MATHEMATICAL SCIENCES, 2020, 10 (02)
  • [5] Little and big q-Jacobi polynomials and the Askey-Wilson algebra
    Baseilhac, Pascal
    Martin, Xavier
    Vinet, Luc
    Zhedanov, Alexei
    [J]. RAMANUJAN JOURNAL, 2020, 51 (03): : 629 - 648
  • [6] Non-classical orthogonality relations for big and little q-Jacobi polynomials
    Moreno, Samuel G.
    Garcia-Caballero, Esther M.
    [J]. JOURNAL OF APPROXIMATION THEORY, 2010, 162 (02) : 303 - 322
  • [7] A LIMIT q =-1 FOR THE BIG q-JACOBI POLYNOMIALS
    Vinet, Luc
    Zhedanov, Alexei
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (10) : 5491 - 5507
  • [8] On ladder operators for little q-Jacobi polynomials and their generalizations
    Filipuk, Galina
    Haneczok, Maciej
    [J]. 2013 15TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND NUMERIC ALGORITHMS FOR SCIENTIFIC COMPUTING (SYNASC 2013), 2014, : 97 - 103
  • [9] Matrix-valued little q-Jacobi polynomials
    Aldenhoven, Noud
    Koelink, Erik
    de los Rios, Ana M.
    [J]. JOURNAL OF APPROXIMATION THEORY, 2015, 193 : 164 - 183
  • [10] Determinantal measures related to big q-Jacobi polynomials
    Gorin, V. E.
    Olshanski, G. I.
    [J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2015, 49 (03) : 214 - 217
12345