- #1
mhill
- 189
- 1
Homework Statement
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] ??
Homework Equations
[tex] g( \alpha ) = \int_{0}^{\infty}dx f(x)Cos( \alpha x) [/tex]
The Attempt at a Solution
where i have used the Euler identity to express the cosine as a linear combination of complex
exponentials.