On some integral transformations and their application to the solution of boundary-value problems in mathematical physics

We obtain a formula for the expansion of an arbitrary function in a series in the eigenfunctions of the Sturm-Liouville boundary-value problem for the differential equation of cone functions. On the basis of this result, we derive a series of integral transformations (including well-known ones) and inversion formulas for them. We apply these formulas to the solution of initial boundary-value problems in the theory of heat conduction for circular hollow cones truncated by spherical surfaces. © 2001 Plenum Publishing Corporation.