If the Fourier cosine transform of  is  , then show that

To prove the given relationship, let's start with the definition of the Fourier cosine transform and use the expression given:

Given that the Fourier cosine transform of \( f(x) \) is \( \alpha^n e^{-a\alpha} \), we can write it as:

\[ F_c[f(x)] = \alpha^n e^{-a\alpha} \]

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