ASYMPTOTICS OF POLLACZEK POLYNOMIALS AND THEIR ZEROS

被引：12

作者：

ISMAIL, MEH

机构：

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1994年 / 25卷 / 02期

关键词：

POLLACZEK POLYNOMIALS; ZEROS; ASYMPTOTICS; CONFLUENT HORN FUNCTIONS;

D O I：

10.1137/S0036141091220293

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An asymptotic expression for the large n behavior of Pollaczek polynomials of degree n and argument cos(theta/square-root n) is derived. This is applied to find the second term in the asymptotic expansion of the zeros of the Pollaczek polynomials and it also solves a problem of Richard Askey. Some new analytic properties of a confluent Horn function are also proved.

引用

页码：462 / 473

页数：12

共 22 条

[1]

[Anonymous], 1953, HIGHER TRANSCENDENTA

[2]

ASKEY RA, 1989, COMMUNICATION JAN

[3]

ASKEY RA, 1984, MEM AM MATH SOC L, V300

[4]

Boas R.P., 1954, ENTIRE FUNCTIONS