# On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics

### Abstract

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.
Published

25.06.2001

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 53, no. 6, June 2001, pp. 810-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4301.

Issue

Section

Research articles