Before revision: We obtain a closed form of generating functions of RNA substructure using hermitian matrix model with the Chebyshev polynomial of the second kind , which has the form of the hypergeometric function .
After revision: Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides, which can be described by random matrix model. We obtain the generating function of the structures using Hermitian matrix model with the Chebyshev polynomial of the second kind , which has the form of the hypergeometric function .