Mathematica Mathematica: Evaluating integral

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The discussion revolves around a challenging integral that the original poster, Niles, has been unable to solve in closed form using Mathematica. Despite successfully completing the two inner integrals, the final integral remains unresolved. A participant suggests a simplified version of the integral, specifically Integrate[(vZ*Erf[vZ]^2)/E^vZ^2, {vZ, 0, Infinity}], indicating that it also lacks a closed form solution. This leads to the conclusion that Niles's original problem likely does not have a closed form solution either.
Niles
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Hi

I need some assistance with the attached integral. I have tried performing it in Mathematica, but it doesn't give me the result in closed form. It just shows the integral.

I have attached my notebook if someone wants to test it out. I would be very happy to receive some feedback as I have spent many hours trying to make this work.


Niles.
 

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It has successfully done the two inner integrals and fails on the final integral.

If I have not made a mistake then a substantially simplified version of your third integral is

Integrate[(vZ*Erf[vZ]^2)/E^vZ^2, {vZ, 0, Infinity}]

and there does not appear to be a closed form solution to that so I do not expect your actual problem has one either.
 
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Thanks, I believe you are right.Niles.
 

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