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

  • G. Ya. Popov

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
PopovG. Y. “On Some Integral Transformations and Their Application to the Solution of Boundary-Value Problems in Mathematical Physics”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 6, June 2001, pp. 810-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4301.
Section
Research articles