Everyone,
Could you help me on the following integral, Many thanks for your help!
$\int\limits_0^\infty {{y^{v - 1}} \cdot \exp \left( { - p{y^a} - q{y^b}} \right)dy} $
where $p>0, q>0$, $a, b$, and $v$ are constant.
2026-05-06 02:10:58.1778033458
Integral of power and exponentials
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The short answer is no. Giving various values to the two exponents a and b, we notice that the result yields completely different types of special functions each time $($ $\Gamma$ functions, Bessel functions, Airy functions, Anger functions, etc. $)$ – and this is only for $a,~b\le4.$ Beyond that, we have hypergeometric series and Meijer G-functions, etc.