\int_0^1\exp[ax-b/(x)]x^{-3/2}dx, where 0<x<1, a>0, b>0.(adsbygoogle = window.adsbygoogle || []).push({});

I know there is no closed form, and it goes to infinity for some value of a and b, but is it able to expresse it by some special functions, like hypergeometric functions?

I checked the math handbooks, could not find any similar forms. Some people suggested using residual theorem which I am not familar with. I tried Monte Carlo simulation and it has nice curve shape that I feel can be expressed by some special functions.

Thanks very much if any one can help!!

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# Can anyone help me with this integral problem?

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