Sums of powers of the zeros of the Bessel polynomials

Abstract

Let σm(n) be the sum of the m‐th powers of the zeros of the Bessel polynomial yn(x). It is known that for m = 0, 1, 2, …, σ−(m+1)(n)=(−1)m+1cm((2n+1)/2), where cm(v) is the Hawkins polynomial. In this paper we find rational functions wm(v) such that for m = 0, 1, 2, … σm+1(n)=(−1)m+1wm((2n+1)/2).