Some generating functions and a projection formula for the associated Askey-Wilson polynomials

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" Some generating functions and a projection formula for the associated Askey-Wilson polynomials "
Q. M. Tariq M. Rahman

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1113451
Doc. No	:	TLpq304361858
Main Entry	:	M. Rahman
	:	Q. M. Tariq
Title & Author	:	Some generating functions and a projection formula for the associated Askey-Wilson polynomials\ Q. M. TariqM. Rahman
College	:	Carleton University (Canada)
Date	:	1997
student score	:	1997
Degree	:	Ph.D.
Page No	:	75
Abstract	:	A generating function for the associated continuous q-Jacobi polynomials is obtained an extension of a result of Gasper and Rahman, and, Bustoz and Ismail. The bilinear generating function (the Poisson kernel) for the associated continuous q-ultraspherical polynomials, first studied by Bustoz and Ismail and later generalized by Ismail and Rahman, is obtained, essentially as a product of a 2\phi\sb1, a 3\phi\sb2 and a 4\phi\sb3 basic hypergeometric series. Some related generating functions are also given. A projection formula for one of the two known families of associated Askey-Wilson polynomials is also obtained by summing an infinite series which exhibits the dual orthogonality of these polynomials in a certain limiting sense. The results also lead to a reproducing kernel for this system of polynomials as well as a weight function for orthogonality.
Subject	:	Mathematics
	:	Pure sciences