IJPAM: Volume 26, No. 2 (2006)

AN ALGORITHM FOR GENERATING MULTI-PARAMETER
WEIGHT FUNCTIONS FOR THE $q^{-1}$-HERMITE
POLYNOMIALS

N.M. Atakishiyev
Instituto de Matemáticas
UNAM - Universidad Nacional Autonoma de Mexico
Apartado Postal 273-3, C.P. 62210
Cuernavaca, Morelos, MEXICO
e-mail: natig@matcuer.unam.mx


Abstract.We discuss an algorithm for generating multi-parameter orthogonality weight functions, both continuous and discrete, for the $q^{-1}$-Hermite polynomials. The key idea is to exploit the general property of these weight functions whereby they are in fact defined only up to multiplication by an arbitrary positive periodic function.

Received: December 12, 2005

AMS Subject Classification: 33D45, 39A13, 42C30

Key Words and Phrases: orthogonality, $q^{-1}$-Hermite polynomials, weight function, theta functions, indeterminate moment problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 2