(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given 2 functions f and g related by a cosine transform

[tex] g( \alpha ) = \int_{0}^{\infty}dx f(x)Cos( \alpha x) [/tex]

then if the integral

[tex] \int_{0}^{\infty}dx f(x)exp(cx) [/tex]

exists for every positive or negative 'c' then should it be equal to

[tex] \int_{0}^{\infty}dx f(x)exp(cx)= \frac{g(ic)+g(-ic)}{2} [/tex] ??

2. Relevant equations

[tex] g( \alpha ) = \int_{0}^{\infty}dx f(x)Cos( \alpha x) [/tex]

3. The attempt at a solution

where i have used the Euler identity to express the cosine as a linear combination of complex

exponentials.

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# Homework Help: Fourier cosine problem

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