On the Zeros of Cross-Product Bessel Functions in Oblique Derivative Boundary-Value Problems

摘要

Combinations of the cross-products of Bessel functions that arise in oblique derivative boundary-value problems for the Laplace operator in a ring are considered. The behavior of zeros of these functions as the ring thickness tends to zero is studied. It is shown that the zeros are divided into two classes, as in the case of Neumann boundary conditions. Some of them remain finite in the limit, while others become infinitely large. Asymptotic expressions for the zeros are found in the case of a fixed inclination angle of the derivative.