Author : Richard Askey
Release : 1984
Genre : Mathematics
Kind : eBook
Book Rating : 019/5 ( reviews)
Book Synopsis Recurrence Relations, Continued Fractions and Orthogonal Polynomials by : Richard Askey
Download or read book Recurrence Relations, Continued Fractions and Orthogonal Polynomials written by Richard Askey. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt: We address the question of recovering the distribution function of a set of orthogonal polynomials from the three term recurrence relation satisfied by the polynomials. We investigate four sets of orthogonal polynomials: the Al-Salam-Chihara polynomials, random walk polynomials and their [italic]q-analogue, and the case [italic]q = -1 of the associated continuous [italic]q-ultraspherical polynomials. For each polynomial set we obtain generating functions, derive explicit representations as ordinary or basic hypergeometric functions and determine their asymptotic behavior