1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Deriving Fresnel Integrals

  1. Mar 5, 2008 #1
    The problem statement, all variables and given/known data
    Integrate [itex]e^{iz^2}[/itex] around the contour C to obtain the Fresnel integrals:

    [tex]\int_0^\infty \cos(x^2) \, dx = \int_0^\infty \sin(x^2) \, dx = \frac{\sqrt{2\pi}}{4}[/tex]

    The contour consists of three parts:

    1. z = x, [itex]0 \le x \le R[/itex]
    2. z = [itex]Re^{i\theta}[/itex], [itex]0 \le \theta \le \pi/4[/itex]
    3. z = [itex]te^{i\pi/4}[/itex], [itex] R \ge t \ge 0[/itex]

    The attempt at a solution
    I'm stumped because I don't know how to evaluate integrals of the form [itex]e^{iz^2}[/itex]. How would I do this?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Deriving Fresnel Integrals
Loading...