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Abstract: We show connections between a special type of addition formulas and a theoremof Stieltjes and Rogers. We use different techniques to derive the desirableaddition formulas. We apply our approach to derive special addition theoremsfor Bessel functions and confluent hypergeometric functions. We also deriveseveral additions theorems for basic hypergeometric functions. Applications tothe evaluation of Hankel determinants are also given .



Author: Mourad E.H. Ismail, Jiang Zeng

Source: https://arxiv.org/







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