Title
Two Variable Extensions Of The Laguerre And Disc Polynomials
Keywords
(Zernike) disc polynomials; 2D-Laguerre polynomials; Combinatorial interpretations; Connection relations; Generating functions; Integrals of products of orthogonal polynomials
Abstract
This work contains a detailed study of a one parameter generalization of the 2. D-Hermite polynomials and a two parameter extension of Zernike's disc polynomials. We derive linear and bilinear generating functions, and explicit formulas for our generalizations and study integrals of products of some of these 2. D orthogonal polynomials. We also establish a combinatorial inequality involving elementary symmetric functions and solve the connection coefficient problem for our polynomials.
Publication Date
4-1-2015
Publication Title
Journal of Mathematical Analysis and Applications
Volume
424
Issue
1
Number of Pages
289-303
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.jmaa.2014.11.015
Copyright Status
Unknown
Socpus ID
84920607060 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84920607060
STARS Citation
Ismail, Mourad E.H. and Zeng, Jiang, "Two Variable Extensions Of The Laguerre And Disc Polynomials" (2015). Scopus Export 2015-2019. 671.
https://stars.library.ucf.edu/scopus2015/671