How to show $L^{-1}(\frac{1}{s^2-1})= J_{0}(t)$
I have deduced that,
$L^{-1}(\frac{1}{s^2-1}) = sinht$
How $sinht$ is related to $J_{0}(t)$. Kindly help
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Aruha
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That's a bit weird, I thought that: $$\mathcal{L}^{-1}\left(\frac{1}{\sqrt{s^2+1}}\right)=J_0(t)$$ You have correctly deduced that $\mathcal{L}^{-1}\left(\frac{1}{s^2-1}\right)=\sinh(t)$. – projectilemotion Feb 13 '20 at 21:02
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how to show $L^{-1}(\frac{1}{\sqrt(s^2+1)})=J_{0}(t)$. kindly show proof – Aruha Feb 13 '20 at 23:58
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See for instance: Laplace transform of Bessel function – projectilemotion Feb 14 '20 at 09:45