Theorem 12.22 (Inverse Laplace Transform).  Let , where are polynomials of degree m and n, respectively, and  .  The inverse Laplace transform of    is given by  

        ,  

where the sum is taken over all the residues of the complex function  .  

Proof.

Proof of Theorem 12.22.

Proof of Theorem 12.22 is in the book.

Complex Analysis for Mathematics and Engineering

(c) 2006 John H. Mathews, Russell W. Howell