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A uniform asymptotic approximation which can be used for all qh > 0 is developed for the Fourier integral z (-,/Y2_ q2) 1(h) = 2 2 1/2 sin yhdy (Y -q ) under the assumptions that hz >> 1, that the first L + 2 derivatives of f(y) are continuous for 0 > q.

An asymptotic approximation for a type of Fourier integral