ABSTRACT
In [177], D. Naylor established a procedure for generating integral transforms adapted to the removal of the polar differential operators that occur when the Laplace differential operator is expressed in either spherical or plane polar coordinates. In so doing, he introduced a set of eight integral transforms that are suited to solve initial and boundary-value problems involving Laplace's operator on regions bounded by the natural coordinate surfaces of cylindrical or spherical coordinate systems. Four of these transforms are suitable for bounded regions and the others for unbounded regions. Naylor called these transforms the finite Mellin-type integral transforms since they are extensions of the Mellin integral transform and their inversion formulas are similar to that of the Mellin transform.
