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How to find the inverse Laplace transformation for given function?

Posted 1 year ago

"I need help: How to find the inverse Laplace transform of this function? The integral variable is s, while others are treated as parameters. Thank you so much!!!"

f1 = a*Subscript[u, 2]/(a^2 + s^2)*Cosh[Subscript[W, 0]*Sqrt[s]*y]
POSTED BY: Aha Aha

Maybe exist closed-from ,but I didn't find it only infinte series.

$\mathcal{L}_s^{-1}\left[\frac{a \cosh \left(\sqrt{s} y \text{W0}\right) \text{u2}}{a^2+s^2}\right](t)=\sum _{m=0}^{\infty } \frac{(-1)^m a^{1+2 m} t^{1+2 m} \text{u2} \, _1F_1\left(-1-2 m;\frac{1}{2};-\frac{\text{W0}^2 y^2}{4 t}\right)}{\Gamma (2+2 m)}$

POSTED BY: Mariusz Iwaniuk
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