- - - Department of applied mathematics, faculty of mathematical sciences, University of Guilan, Rasht-Iran, P. O. Box ۱۸۴۱

In this article, we will show the complex inversion formula for the inversion of the L۲-transform and also some applications of the L۲, 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.

L۲-Transform, Laplace transform, Complex inversion formula, Post-Widder transform