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Math Help - Kac Formula plot with MatLab

  1. #1
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    Kac Formula plot with MatLab

    I am trying to plot the Kac Formula with MatLab and I am having trouble.
    Here's a link to the formula
    Kac Formula -- from Wolfram MathWorld
    Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by YankeesFan View Post
    I am trying to plot the Kac Formula with MatLab and I am having trouble.
    Here's a link to the formula
    Kac Formula -- from Wolfram MathWorld
    Any help would be greatly appreciated.
    First you write a function to evaluate I_n(t), Now we want:

    E_n=\frac{1}{\pi}\int_{-\infty}^{\infty}I_n(t)\; dt

    In order to get rid of the infinite range of integration we make a change of variable: u=\arctan(t) and the integral becomes:

    E_n=\frac{1}{\pi}\int_{-\pi/2}^{\pi/2}\frac{I_n(\tan(u))}{\cos^2(u)}\; du

    Now you use Matlab quad function to evaluate this.

    CB
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