Curious Relations and Identities Involving the Catalan Generating Function and Numbers
نویسندگان
چکیده
Riordan matrix methods and manipulation of various generating functions are used to find curious relations among the Catalan, central binomial, and RNA generating functions. In addition, the Wilf-Zeilberger method is used to find identities where the gamma function and Catalan numbers are expressed in terms of the Gauss hypergeometric function. As a consequence of the identities, new recurrence relations are obtained. In particular, a new recurrence relation is given for the RNA numbers. Furthermore, other representations of π and the Catalan numbers are obtained.
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