ABSTRACT
The Mehler-Fock transformation, which was introduced by V. Fock in 1943 [64], is particularly useful in solving many problems in elasticity theory, where axial symmetry is present or toroidal coordinates are used. It has also been used in mechanics and fluid dynamics [30] to solve some problems with mixed boundary conditions. One of its drawbacks, however, is that calculating it explicitly is rather difficult; the transforms of only a few functions can be calculated in closed form.
