Laplace transform of a series in time t

[sarrah1]

Hi

I have a series

${f}_{1}$ , ${f}_{2}$, ... that are all a functions of a variable $t$

I am seeking a point-wise convergence. to investigate the convergence of the series I took Laplace transform. If I can find a condition on the Laplace variable $s$, can I find the condition of convergence of the series on $t$.

is it normal to investigate convergence of series via Laplace transform ?
thanks

 

[Jhoneine]

Yes, it is normal to investigate the convergence of a series via Laplace transform. The Laplace transform can be used to determine the conditions on the Laplace variable $s$ for which the series converges. This then allows us to determine the conditions on the original variable $t$ for which the series converges.

 

[math771]

Hi there,

It is not uncommon to use the Laplace transform to investigate the convergence of a series. The Laplace transform can be a useful tool in determining the behavior of a series, particularly in terms of its rate of convergence. However, it is not the only method and may not always be the most appropriate approach depending on the specific series and its properties. It is always a good idea to explore different methods and techniques to get a better understanding of the convergence of a series. Hope this helps!