Question
Obtain the Fourier cosine transformation of the function:
Answer :
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The Fourier cosine transform of a function ( f(x) ) defined on ( (0,\infty) ) is given by [ F_c(\omega)=\sqrt{\frac{2}{\pi}}\int_{0}^{\infty} f(x)\cos(\omega x),dx . ] Here ( f(x)=e^{-px} ) with ( p>0 ). Substituting, [
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