Hi! How do I approximate the integral(adsbygoogle = window.adsbygoogle || []).push({});

\begin{equation} \int_0^{\infty} dt \:e^{-iA(t-B)^2} \end{equation}

with [itex]A, B[/itex] real, [itex]A > 0[/itex], and [itex]B=b \cos\theta[/itex] where [itex]0 \leq \theta < 2\pi[/itex]?

I guess for [itex] B\ll 0[/itex] the lower limit may be extended to [itex] - \infty[/itex] to yield a full complex gaussian integral, but what about [itex]B \geq 0[/itex]? And what happens for [itex]A \gg 1[/itex] and [itex]A \ll 1[/itex] respectively?

Thanks for your help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Approximation of error function-type integral

**Physics Forums | Science Articles, Homework Help, Discussion**