MHB Laplace transform of a series in time t

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Investigating the convergence of a series of functions using the Laplace transform is a standard approach. By analyzing the Laplace variable \( s \), one can establish conditions for the convergence of the series. These conditions can then be translated to the original variable \( t \). This method effectively links the behavior of the series in the time domain to its representation in the Laplace domain. Utilizing the Laplace transform for this purpose is both normal and beneficial in mathematical analysis.
sarrah1
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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
 
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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.
 

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