Continued fractions related to Narayana polynomials

TL;DR

This paper explores continued fraction representations of generating functions for Catalan numbers, Narayana polynomials, and q-Narayana polynomials at q=-1, providing new insights into their structure.

Contribution

It presents new continued fraction expansions for q-Narayana polynomials at q=-1, extending known results for classical sequences.

Findings

Continued fraction expansions for Catalan and Narayana generating functions

Analogous continued fractions for q-Narayana polynomials at q=-1

Overview of simple continued fraction expansions for these sequences

Abstract

The generating functions of some sequences of Catalan numbers and Narayana polynomials have simple expansions as continued fractions of Jacobi type. We give an overview of these facts and prove analogous results for q-Narayana polynomials at q=-1.