Distribution of zeros of the relativistic Hermite polynomials

Abstract

We will consider the second order differential equation ◁수식 삽입▷(원문을 참조하세요) Their polynomial solutions are commonly known as relativistic Hermite polynomials(RHP),which is denoted by $H_n^{(N)}(ξ)$. In this paper, we obtain the true moments of the RHP. Moreover, a study of the zero distribution of the RHP is done within the so-called WKB(or semiclassical) approximation. Specifically, the WKB density of zeros of the RHP is obtained analytically in a closed way in terms of the coefficients of the differential equation that they satisfy.