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.
2차 미분방정식
◁수식 삽입▷(원문을 참조하세요)
의 다항식해는 relativistic Hermite 다항식으로 알려져 있다.
여기서는 미분방정식(*)의 계수들에 의해서 재귀적으로 생성되어지는 모멘트를 얻었고, WKB 방법을 이용하여 relativistic Hermite 다항식의 zero distribution을 구했다.
