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Bessel function with e^(x^2)

  1. Dec 12, 2011 #1

    ibw

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    I am doing a research degree in optical fields and ended up with the following integral in my math model. can you suggest any method to evaluate this integral please. Thanks in advance

    ∫(j(x) *e^(ax^2+ibx^2) dx


    J --> zero order bessel function
    i--. complex
    a & b --> constants
     
  2. jcsd
  3. Dec 24, 2011 #2
    If the limits are from 0 to infinity it can be easily evaluated using Webers double integral.
    for other limits I dont think a close form exists.
    Check: Watson: A treatise on the theory of Bessel functions
    for more details
     
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