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Derive the Laplace Transform of $I_0(\alpha t)$

Using the definition of Laplace Transform and also using Modified Bessel Function as Definition . Since the Modified Bessel function of the first kind is $I_n(z)$, n is equal to zero and $z$ will be equal to $\alpha t$. Derive its Laplace Transform.

http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html

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Since the wording of the question is very short, the wording of the answer is short as well : $$\mathcal{L}_t\left(\text{I}_0(\alpha t)\right)(p)=\frac{1}{p^2-\alpha^2}$$

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    I edited the question, hope it helps. – 2017-02-15
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    I need the step by step solution for the problem, using the definition of the Modified Bessel function as stated above. Thank you btw. – 2017-02-15
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    Sorry, to comply to the rules of the forum I am not allowed to give a step by step solution until your question be not marked "on hold". – 2017-02-15