In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

is obtained by applying successive integration by parts to the integral represented by the left-hand member of this equation so that the new integrand is the product of F by [(1 —x2)P„' ]', and by replacing this second factor by — n(n + l)Pn according to Legendre's differential equation [l]. Thus certain boundary value problems in ordinary and partial differential equations that involve the dif...