ASYMPTOTICS OF POLLACZEK POLYNOMIALS AND THEIR ZEROS

Authors
ISMAIL MEH
Citation
Meh. Ismail, ASYMPTOTICS OF POLLACZEK POLYNOMIALS AND THEIR ZEROS, SIAM journal on mathematical analysis, 25(2), 1994, pp. 462-473
Citations number
22
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM journal on mathematical analysis → ACNP
ISSN journal
00361410
Volume
25
Issue
2
Year of publication
1994
Pages
462 - 473
Database
ISI
SICI code
0036-1410(1994)25:2<462:AOPPAT>2.0.ZU;2-2
Abstract
An asymptotic expression for the large n behavior of Pollaczek polynom ials of degree n and argument cos(theta/square-root n) is derived. Thi s is applied to find the second term in the asymptotic expansion of th e zeros of the Pollaczek polynomials and it also solves a problem of R ichard Askey. Some new analytic properties of a confluent Horn functio n are also proved.