One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition.

In this paper, we consider the spectral problem for the semi-integer Bessel equation with a boundary condition containing the square of the spectral parameter and a complex physical parameter. The system of eigenfunctions of the problem and the characteristic equation for the eigenvalues are derived. The equation for multiple roots of the characteristic equation is derived. The results on the basis properties (Riesz basis) of the system of eigenfunctions at different values of the parameter are obtained. For each case a biorthogonally conjugate system is constructed. At the end of the paper there is an example for the order of Bessel functions equal to . [ABSTRACT FROM AUTHOR]