Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions

• DOI: 10.1186/s40064-015-1142-0
• Publication Date: 2015-08-03T09:04:07Z
• Authors: Christian H Ziener; Felix T Kurz; Lukas R Buschle; Thomas Kampf
• Keywords: Orthogonality; Eigenfunction; Complex plane

The cylindrical Bessel differential equation and the spherical in interval [Formula: see text] with Neumann boundary conditions are considered. eigenfunctions linear combinations of function or functions text]. orthogonality relations analytical expressions for normalization constant given. Explicit Lommel integrals terms derived. cross product zeros considered complex plane real as well values index approximations exceptional zero obtained. A numerical scheme based on discretization two-dimensional three-dimensional Laplace operator is presented. representations radial part form a tridiagonal matrix allow simple computation zeros.