ADDITION THEOREMS VIA CONTINUED FRACTIONS
Abbreviated Journal Title
Trans. Am. Math. Soc.
Addition theorems; orthogonal polynomials; continued J-fractions; q-orthogonal polynomials; Askey-Wilson polynomials; Bessel and confluent; hypergeometric functions; HANKEL DETERMINANTS; POLYNOMIALS; Mathematics
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.
Transactions of the American Mathematical Society
"ADDITION THEOREMS VIA CONTINUED FRACTIONS" (2010). Faculty Bibliography 2010s. 292.