The Funk‐Hecke type relations and ray transforms for the vector spherical wave functions.

The Funk‐Hecke type integral relations for vector spherical wave functions are derived. Applying the obtained Funk‐Hecke integral identities, 3D Fourier transforms of vector spherical wave functions Mlmτ and Nlmτ and Llmτ are obtained. On the basis of the Central Slice Theorem, the ray transforms for these vector functions are evaluated. This was found to be a useful tool in the scattering and the vector tomography problems. [ABSTRACT FROM AUTHOR]