# Tagged Questions

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### Mellin transform of time-shifted function

The Mellin transform of a function $f(x)$ can be written as $$\mathcal M[f(x);z]=\int_0^\infty f(x)x^{z-1} dx$$ Is there a simple expression for the Mellin transform of the function $f(x-x_0)$? ...
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### Uncertainty principle for Mellin transform

Let $f:\mathbb{R}^+\to \mathbb{C}$. Let $Mf$ be its Mellin transform: $Mf(s) = \int_0^\infty f(x) x^{s-1} dx$. (a) Some time ago, I convinced myself that $f(t)$, $Mf(\sigma+it)$ and $Mf(\sigma-it)$ ...
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### Does the inverse Laplace transform of the square root exist?

Does the inverse Laplace transform, defined by the integral, $$F(t) = \mathscr L_s^{-1}\left[\sqrt s\right](t) = \int_{c - i\infty}^{c + i\infty} \sqrt s ~e^{-st} ds$$ ...
839 views

### An inverse Laplace transform involving Error function

Dear MOs, I need to calculate the inverse Laplace transform of the following function $$g_a(z) = \frac{e^{a z}\: \text{erfc}(\sqrt{a z})}{\sqrt{z}-2},\quad a>0.$$ I have checked, among many ...
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### On the generalisation of the Laplace transform

I consider a measure transform $A$ given by $$A\mu(x) = \int\limits_{\mathbb{R}^n_{+}} e^{-g(x,y)} \mu(dy)$$ where $g(x,y)$ is some positive smooth function, $\mu$ is a Borel measure. Is it a ...
### Stieltjes Transform of $F^{*}PF$ as a function of the Stieltjes Transform of $P$ where $F$ is drawn from an $n \times n$ Gaussian-like random matrix distribution
I am trying to calculate the Stieltjes Transform of $F^{*}PF$ as a function of the Stieltjes Transform of $P$ where $F$ is drawn from an $n \times n$ Gaussian-like random matrix distribution. I am ...