Complex zeros of Bessel function derivatives and associated orthogonal polynomials

We introduce a sequence of orthogonal polynomials whose associated moments are the Rayleigh-type sums, involving the zeros of the Bessel derivative J_ν' of order ν. We also discuss the fundamental properties of those polynomials such as recurrence, orthogonality, etc. Consequently, we obtain a formula for the Hankel determinant, elements of which are chosen as the aforementioned Rayleigh-type sums. As an application, we complete the Hurwitz-type theorem for J_ν', which deals with the number of complex zeros of J_ν' depending on the range of ν.