Probabilistic aspects of Al-Salam-Chihara polynomials

被引：30
作者：
Bryc, W
Matysiak, W
Szablowski, PJ
机构：
[1] Univ Cincinnati, Dept Math, Cincinnati, OH 45221 USA
[2] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 04期
关键词：
q-Hermite polynomials; matrix of moments; orthogonal polynomials; determinants; polynomial regression;
D O I：
10.1090/S0002-9939-04-07593-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We solve the connection coefficient problem between the Al-Salam-Chihara polynomials and the q-Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some Al-Salam-Chihara polynomials, and compute determinants of related Hankel matrices.
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页码：1127 / 1134
页数：8
相关论文
共 14 条
[1]   CONVOLUTIONS OF ORTHONORMAL POLYNOMIALS [J].
ALSALAM, WA ;
CHIHARA, TS .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1976, 7 (01) :16-28
[2]  
ASKEY R, 1984, MEM AM MATH SOC, V49, P1
[3]  
ASKEY R, 1989, IMA VOL MATH APPL, V18, P151
[4]   Q-hermite polynomials and classical orthogonal polynomials [J].
Berg, C ;
Ismail, MEH .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1996, 48 (01) :43-63
[5]   Stationary random fields with linear regressions [J].
Bryc, W .
ANNALS OF PROBABILITY, 2001, 29 (01) :504-519
[6]  
Carlitz L., 1955, ANN MAT PUR APPL, V41, P359, DOI DOI 10.1007/BF02411676
[7]  
Freud G., 1971, ORTHOGONAL POLYNOMIA
[8]   THE COMBINATORICS OF Q-HERMITE POLYNOMIALS AND THE ASKEY-WILSON INTEGRAL [J].
ISMAIL, MEH ;
STANTON, D ;
VIENNOT, G .
EUROPEAN JOURNAL OF COMBINATORICS, 1987, 8 (04) :379-392
[9]   Q-HERMITE POLYNOMIALS, BIORTHOGONAL RATIONAL FUNCTIONS, AND Q-BETA-INTEGRALS [J].
ISMAIL, MEH ;
MASSON, DR .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 346 (01) :63-116
[10]  
Krattenthaler C., 1999, SEM LOTHAR COMB, V42
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