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Hi! How do I approximate the integral

\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!

\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!

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