Title
ADDITION THEOREMS VIA CONTINUED FRACTIONS
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
ISSN
0002-9947
Recommended Citation
"ADDITION THEOREMS VIA CONTINUED FRACTIONS" (2010). Faculty Bibliography 2010s. 292.
https://stars.library.ucf.edu/facultybib2010/292
Comments
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