HOw can you evaluate (for big 'u') the exponential integral(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{0}^{1}dx f(x)e^{iux} [/tex] u-->oo

if you use Numerical methods, since exp(iux) oscillates rapidly you cannot apply any of them, also since we have inside exponential (iux) you can not apply 'Stationary phase method' unless you make the change.

[tex] \int f(g(t)exp(iug(t)) [/tex]

and then apply stationary phase finding [tex] g'(t)=0 [/tex] to evaluate the integral but i am not pretty sure.

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# Evaluation of oscillatory integrals

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