Recent content by kaniello

Dear I like Serena, thanks a lot for your reply. Which library did you use to perform the sine transform of ## xe^{-x^2} ## ? It would be really interesting to compare the results. I do not apply any filter to my Input data but I will try to understand from the FFTw Website if it is somehow...

Sorry for the typing error,of course the the correct argument $$\sin \left(\omega x \right)$$. The resolution is still poor even with 256 points Can anybody tell me where the deviation between 2.0 and 7.0 comes from? (please see attachments).

Hi mathman, the original equation is $$ f(x) = x \cdot e^{-x^2}$$ . Its analytical sine-transform is given by $$ \mathcal{F}_s \lbrace f(x) \rbrace (\omega) = \int\limits_{0}^{\infty } x \cdot e^{-x^2} \cdot \sin\left(x\right)\, \mathrm{d}x = \frac{1}{2} \pi^2 \omega e^{- \frac{1}{4} \pi^2...

Hello Scottdave, thank you very much for your hint, my post looks definitely better now. I hope that you can see the attachments now

Hi, I am a neophyte in Discrete Fourier Transform and I am procticing with discrete Sine-transform. Specifically I want to calculate $$ \mathcal{F}_s \lbrace x \cdot e^{-x^2} \rbrace = \int\limits_{0}^{\infty } x \cdot e^{-x^2} \cdot \sin\left(x\right)\, \mathrm{d}x = \frac{1}{2} \pi^2 \omega...

Hi blue_leaf77, so, up to now we have proven that the result ##\mathcal{I}=\int_{-\infty }^{+\infty }\frac{f\left ( \left | \vec{x} \right | \right )}{\left | \vec{c}-\vec{x} \right |}d^{3}x = \frac{1}{c}\int_{0}^{c}fx^{2}dx+\int_{c}^{\infty }fxdx## is correct. Still my question is : how can...

The integral in ##\vartheta## returns $$\sqrt{c^{2}+x^{2}-2cx}-\sqrt{c^{2}+x^{2}+2cx}$$ which must be inserted in the integral in ##x## taking care to break the integral into ##0\leqslant x < c## and ##c< x < \infty ## due to the first radicand. If ##c=0## from the original integral one gets...

Thanks a lot for the explanation. With that hint I repeated the calculations and found: ##\int_{0}^{\infty }\int_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\frac{f\left ( x \right )}{\sqrt{c^{2}+x^{2}-2cx\sin \vartheta }}x^{2}\cos \vartheta d\vartheta dx=\int_{0}^{\infty }f\left ( x \right...

My intention was in fact to place the red lines in the plane ##x_1 x_2## so that it forms the angle ##\theta## with ##\vec x##. As you suggested ##\vec x## should be in the plane ##\vec c## x_3## axis.

What if pick the red line?

This is maybe more clear

I did my best to draw it [emoji6]

Hello and sorry for not being online yesterday. Can you please explain me better what do you mean by :

Dear "General Math" Community, my goal is to calculate the following integral $$\mathcal{I} = \int_{-\infty }^{+\infty }\frac{f\left ( \mathbf{\vec{x}} \right )}{\left | \mathbf{\vec{c}}- \mathbf{\vec{x}} \right |}d^{3}x $$ in the particular case in which f\left ( \mathbf{\vec{x}} \right...

Hallo, I posted this in General Math, and I decided to post it here also because this room seems more appropriate. The formulas and part of the text are quoted from "Klimontovich - Statistical theory of non-equilibrium processes in a plasma": Let N_{a}(\textbf{x},t)...