عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
TLpq304361858
انگلیسی
Some generating functions and a projection formula for the associated Askey-Wilson polynomials
[Thesis]
Q. M. Tariq
M. Rahman
Carleton University (Canada)
1997
75
Ph.D.
Carleton University (Canada)
1997
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.
Mathematics
Pure sciences
M. Rahman
Q. M. Tariq
مطالعه متن کتاب p
[Thesis]
276903
a
Y
