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Math Help - Which Contour: Rectangle or Semi-Circle?

  1. #1
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    Which Contour: Rectangle or Semi-Circle?

    When evaluating a real integral over the real axis (i.e. -infty to + infty) using methods of contour integration, are there any hard and fast rules regarding the integrand which may help in deciding whether to use a Rectangular or a Circular contour, for example?
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  2. #2
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    Nobody can help, huh?
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  3. #3
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    Quote Originally Posted by Jippo
    Nobody can help, huh?
    Symmetry is often a good guide.

    RonL
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  4. #4
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    Quote Originally Posted by Jippo
    Rectangular or a Circular contour, for example?
    I prefer using a semi-circle.
    Because, if you use squares you have,
    \lim_{n\to\infty} \int^n \int^n
    In semi-circles, there is only one variable tending to infinity,
    \lim_{r\to\infty} \int_{-\pi/2}^{\pi/2} \int^r_0
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  5. #5
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    Quote Originally Posted by ThePerfectHacker
    I prefer using a semi-circle.
    Because, if you use squares you have,
    \lim_{n\to\infty} \int^n \int^n
    In semi-circles, there is only one variable tending to infinity,
    \lim_{r\to\infty} \int_{-\pi/2}^{\pi/2} \int^r_0
    if you have symmetry you can cancel two sides of thesquare.

    RonL
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