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Can't figure out why Mathematica doesn't want to execute built-in functions? What can be wrong?

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Input:

Convolve[1/(x - t)^(3/2)*Exp[-gamma/(2 (x - t))], 1/t^(3/2)*Exp[-gamma/(2 t)], t, x]

Output:

Convolve[E^(-(gamma/(2 (-t + x))))/(-t + x)^(3/2), E^(-(gamma/(2 t)))/t^(3/2), t, x]

Input:

Integrate[(1/(x - t)^(3/2)*Exp[-gamma/(2 (x - t))])*(1/t^(3/2)*
Exp[-gamma/(2 t)]), t]

Output:

\[Integral]E^(-(gamma/(2 t)) - gamma/(2 (-t + x)))/(t^(3/2) (-t + x)^(3/2)) \[DifferentialD]t
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    $\begingroup$ Likely, that means Mathematica doesn't know a closed-form solution, if it exists. $\endgroup$ – J. M. is away Apr 1 '18 at 13:17
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    $\begingroup$ And when asking questions, post code rather than pictures of code so that people can copy and paste the code into a workbook. $\endgroup$ – Bob Hanlon Apr 1 '18 at 13:34
  • $\begingroup$ @BobHanlon, thanks for advice, I have added source code too and will do it further. $\endgroup$ – Hasek Apr 1 '18 at 13:57
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The problem that you having with your problem is that the convolution envelope does not converge well when approaching zero. The best way is tackle this is to add a step function. This way will force all envelope to be zero for all negative numbers. Inspecting the envelope with Gamma = 1 Plot[1/t^(3/2)*Exp[-1/(2 t)] UnitStep[t], {t, -2, 2}]

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Follow up with the convolution

ClearAll["Global`*"]

Convolve[1/(x - t)^(3/2)*Exp[-\[CapitalGamma]/(2 (x - t))], 
 1/t^(3/2)*Exp[-\[CapitalGamma]/(2 t)] UnitStep[t], t, x]

The result is $ \frac{1}{\Gamma ^2} $

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