Finding Laplace inverse transformation of a product series [closed]

compute the inverse Laplace transformation of the following equation.

\begin{align*} f(s)&=\frac{A}{\prod_{i=1}^{L}(s+a_i)^m} \\ &=\frac{A}{(s+a_1)^m\,(s+a_2)^m\cdots (s+a_L)^m}. \end{align*}

What I managed to get is this \begin{align*} Y^{-1}(\frac{1}{(s+a)^m})&=\frac{t^{m-1}e^{-at}}{{(m-1)!}} \end{align*}

How do I find the Laplace inverse of the series though? Someone suggested me using partial fraction decomposition and gave me this solution, \begin{align*}f(s)=\sum_{1\le k\le m\atop 1\le j\le L} {A_{jk}\over(s+a_j)^k}\end{align*} But failed to tell how did we achieve it.

New contributor
Viplav Prakash is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

closed as off-topic by Pietro Majer, j.c., Stefan Kohl, Carlo Beenakker, Jan-Christoph Schlage-PuchtaSep 15 at 18:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – j.c., Stefan Kohl
If this question can be reworded to fit the rules in the help center, please edit the question.

• Welcome to MathOverflow! MathOverflow is for mathematicians to ask each other questions about their research. See Mathematics to ask general questions in mathematics. – Glorfindel Sep 14 at 13:04
• – jeq Sep 14 at 15:27