# Tagged Questions

This covers all transformations of functions by integrals, including but not limited to the Radon, X-Ray, Hilbert, Mellin transforms. Use (wavelet-transform), (laplace-transform) for those respective transforms, and use (fourier-analysis) for questions about the Fourier and Fourier-sine/cosine ...

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### Evaluating Laplace Transform

I have a Laplace transform function of the following form and I'm trying to evaluate it. From my research I think I need to take the Inverse Laplace Transform and then integrate, but I'm having ...
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### Evaluating improper integrals using laplace transform

I want to calculate the following improper integral using Laplace and transforms (and laplace transforms only). $$\int_0^{\infty} x e^{-3x} \sin{x}\, dx$$ I propose the following method. I plan to ...
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### Showing a Hölder continuous function acted on by a singular integral operator is Hölder continuous

Consider the following function defined by a singular integral F(x)= \lim_{\epsilon \rightarrow 0} \int_{|x-y| \geq \epsilon} \partial_k \partial_j k_i(x-y) \left(Y_k(x)- Y_k(y) \...
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### nonlinear integral equation

let be the integral equation for two functions $f(x)$ and $g(x)$ in the form $$g(s)= \int_{0}^{s}\sqrt{s-f(x)}dx$$ is valid to accept that in the sense of fractional calculus, the ONLY ...
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### Double Integral involving modifed bessel function

I'm try to derive a closed form of the following double integral: $\int\limits_0^x {\int\limits_0^x {{e^{ - {K_1}uv}}{I_0}\left( {2{K_1}\sqrt {uv} } \right)du} dv}$; where $K_1$ is a constant. Do you ...
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### arguing away - complex analysis

Probably a trivial question but I can't understand how to argue away the value of integrals in complex analysis. I am trying to find the inverse Laplace transform of $F(s)=\frac{1}{s(s+1)}$. The ...
I am seeking a function $f(x)$ that satisfies this condition: $\int_{0}^{\infty }f(x)x^ndx=\sqrt{n!}$ where n is an integer. I guess that $f$ will contain $e^{-\alpha x^2}$ as one of its factors, ...
maple code int(g*f, x=-infinity..infinity) when $g$ is $\large exp^{i*t*x}$, Fourier transform between density function and characteristic function If $g$ are $x^t$, $|x^{t}|$, $t^{x}$, what do they ...