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.