Two variable extensions of the Laguerre and disc polynomials
Abbreviated Journal Title
J. Math. Anal. Appl.
2D-Laguerre polynomials; (Zernike) disc polynomials; Integrals of; products of orthogonal; polynomials Generating functions; Connection; relations; Combinatorial interpretations; ORTHOGONAL POLYNOMIALS; ZERNIKE; Mathematics, Applied; Mathematics
This work contains a detailed study of a one parameter generalization of the 2D-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 2D orthogonal polynomials. We also establish a combinatorial inequality involving elementary symmetric functions and solve the connection coefficient problem for our polynomials. (C) 2014 Elsevier Inc. All rights reserved.
Journal of Mathematical Analysis and Applications
"Two variable extensions of the Laguerre and disc polynomials" (2015). Faculty Bibliography 2010s. 6597.