# Tagged Questions

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### Scary contour integral, but is also an integral representation for $\Gamma$-function

This problem is supposed to be from an old Acta Mathematica volume I circa 1880's, and is attributed to Bourguet. By using a parabola with its focus on the origin as a contour, show that: ...
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### Integral / Gamma Expectation

I would like to solve the following integral, $\int_{0}^{\infty}\frac{\phi}{a+b\phi} \phi^{c-1}e^{-d\phi}d\phi$. Note $\phi \sim Ga(c,d)$ is a gamma distributed random variable and the integral can ...
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### complex integral of z to the power alpha

I would like to perform an inverse laplace and at some point of the calculation I have to compute this integral $$\int_{\gamma-i\infty}^{\gamma+i\infty} z^{(1+n)\alpha-1}e^{z} \frac{dz}{2\pi i}$$ ...
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### Gamma Function Contour Integration

So, I've been trying to prove the following integral related to the gamma function, and I'm really banging my head against the wall over this: ...
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### half-line Fourier transform of $x^{z-1}$ w.r.t. $x$?
Can someone help me evaluate $G_g(z)=\int_0^{\infty}x^{z-1}e^{igx}dx$, where $g$ is real and $z$ is complex? By closing the contour in the upper half plane, I've managed to prove that if ...
Let $\epsilon > 0$, and $n \in \mathbb{Z}^{+}$. Let $C_{n}$ be a positively oriented polygonal line that is from $-n + 1/2 - i \epsilon$ to $1/2 - i \epsilon$ and from $1/2 - i \epsilon$ to \$ ...