Title

ADDITION THEOREMS VIA CONTINUED FRACTIONS

Authors

Authors

M. E. H. Ismail;J. Zeng

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Trans. Am. Math. Soc.

Keywords

Addition theorems; orthogonal polynomials; continued J-fractions; q-orthogonal polynomials; Askey-Wilson polynomials; Bessel and confluent; hypergeometric functions; HANKEL DETERMINANTS; POLYNOMIALS; Mathematics

Abstract

We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for Bessel functions and confluent hypergeometric functions. We also derive several addition theorems for basic hypergeometric functions. Applications to the evaluation of Hankel determinants are also given.

Journal Title

Transactions of the American Mathematical Society

Volume

362

Issue/Number

2

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

957

Last Page

983

WOS Identifier

WOS:000274739600016

ISSN

0002-9947

Share

COinS