A problem about integral of modified bessel function

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The discussion focuses on the need to compute the inverse Laplace transform of a product of modified Bessel functions, specifically involving the expression abs^2 K_n(√as) K_n(√bs). The user is seeking assistance with properties of Bessel functions that could facilitate solving this integral. There is an emphasis on finding the correct approach to handle the integral for calculating the probability density function of a random variable. The community is invited to provide insights or solutions related to the inverse Laplace transform of modified Bessel functions. Overall, the thread highlights a mathematical challenge involving special functions in probability theory.
jianingli
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To calculate a p.d.f. of a r.v., I need to integral a product of two bessel function as

\mathcal{L}^{-1} \left( abs^2 K_n( \sqrt{as}) K_n( \sqrt{bs} ) \right)

where \mathcal{L}^{-1} is the inverse Laplace transform.

I think some properties about the bessel function can solve this integral, but I cannot find it. So, please help me.

Thank you very much.
 
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I am looking for the inverse laplace transform of modified Bessel functions, could you please help me?.
 

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