Some identities for the Narayana polynomial and its derivatives

TL;DR

This paper derives new mathematical identities for the Narayana polynomial and its derivatives using properties of semicircular distributions, contributing to combinatorial and probabilistic theory.

Contribution

It introduces novel identities for the Narayana polynomial and derivatives by leveraging properties of semicircular distributions, expanding theoretical understanding.

Findings

New identities for Narayana polynomial derived

Connections established between polynomials and semicircular distributions

Potential applications in combinatorics and probability

Abstract

In this note, by employing a nice property of semicircular distributions, we derive some identities for the Narayana polynomial and its derivatives.