I have an integral like(adsbygoogle = window.adsbygoogle || []).push({});

[tex]F(\lambda)=\int_{-\infty}^\infty e^{i\lambda x} f(x) dx,[/tex]

where [itex]\lambda[/itex] is a real parameter and [itex]f(x)[/itex] is an integrable function of x. I am looking for a method to calculate an approximate form of [itex]F(\lambda)[/itex] for very small [itex]|\lambda|[/itex]. Methods like stationary phases or steepest descent can sometimes be used to calculate similar asymptotic expressions for large values of the parameter, but I am not sure how to proceed in case [itex]\lambda[/itex] is small.

Thanks.

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# Asymptotic form of Fourier type integral

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