Question

If the Fourier cosine transform of f(x) is equation, then show that


equation

09 Jan 2026
Answer :
Word Count : 248
We are asked to find (f(x)) given its Fourier cosine transform: [ F_c{f(x)} = \int_0^\infty f(x) \cos(\alpha x) , dx = \alpha^n e^{-a \alpha}. ] The inverse Fourier cosine transform formula is: [ f(x) = \frac{2}{\pi} \int_0^\infty F_c{f(x)} \cos(\alpha x) , d\alpha = \frac{2}{\pi} \int_0^\infty \alpha^n e^{-a \alpha} \cos(\alpha x)
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