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Hi all.

I have the following Fourier transformation:

[tex]

u(x,t) = \sqrt {\frac{2}{\pi }} \int_0^\infty {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}

\over f} _s (\omega )\,e^{ - c^2 \omega ^2 t} \sin \omega x\,d\omega },

[/tex]

where f_{s}is the sine-transform of a functionf. I am supposed to rewrite this into the form:

[tex]

u(x,t) = \frac{1}{{2c\sqrt {\pi t} }}\int_0^\infty {f(s)\left[ {\exp \left( { - \frac{{(x - s)^2 }}{{4c^2 t}}} \right) - \exp \left( { - \frac{{(x + s)^2 }}{{4c^2 t}}} \right)} \right]} \,ds

[/tex]

I can see I have to start working with the sine transform off. But I don't know what to write this as?

Thanks in advance,

sincerely Niles.

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# Homework Help: Fourier Transformations: Rewriting a F.T.

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