# Technical question about a Fourier transform

I would like to know if there is an explicit expression for the Fourier transform of the following function: $$f(x)=\mathbb{1}_{(0,\infty)}e^{-x-ix^2},$$ or to know where I can find some techniques to have some asymptotical expansion of such Fourier transform.

• it's a Fresnel integral Jun 5, 2015 at 11:12
• Thanks. I noticed it, but are there some explicit expression for these integrals? Jun 5, 2015 at 11:50
• well, it's called a Fresnel integral because it cannot be written in terms of elementary functions (very much like the error function) Jun 5, 2015 at 11:53
• Doesn't repeated integration by parts of the Fourier transform integral give an asymptotic expansion? Jun 5, 2015 at 14:36