Quadratures and integral transforms arising from generating functions

被引：2
|
作者：
Campos, Rafael G. [1 ]
Marcellan, Francisco [2 ,3 ]
机构：
[1] Univ Michoacana, Fac Ciencias Fisicomatemat, Morelia 58060, Michoacan, Mexico
[2] Univ Carlos III Madrid, Inst Ciencias Matemat ICMAT, Leganes 28911, Spain
[3] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2017年 / 297卷
关键词：
Integral transforms; Quadratures; Orthogonal polynomials; Generating functions; STATES;
D O I：
10.1016/j.amc.2016.11.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By using the explicit form of the eigenvectors of the finite Jacobi matrix associated to a family of orthogonal polynomials and some asymptotic expressions, we obtain quadrature formulas for the integral transforms arising from linear generating functions of the classical orthogonal polynomials. As a bypass product, we obtain simple and accurate Riemann-Steklov quadrature formulas and as an application of this quadrature formalism, we obtain the relationship between the fractional Fourier transform and the canonical coherent states. (C) 2016 Elsevier Inc. All rights reserved.
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页码：8 / 18
页数：11
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