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Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

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Is there a way to get the closed form approximate result of $\int_ 0^a\frac {e^{-x - \frac {... [closed]

It is known that $$\int_ 0^{\infty}\frac {e^{-x - \frac {1} {x}}} {x} dx=2 K_0(2),$$ but now I want to get the closed form approximate result of $$\int_ 0^a\frac {e^{-x - \frac {1} {x}}} {x} dx.$$ I …