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Math Help - [SOLVED] Need to solve

  1. #1
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    [SOLVED] Need to solve

    Hi All, Could any one please help me solve this.

    I have big expression with sin(x) and cos(x), which resulted after integrating another function. I need to apply the <br />
\lim_{x\to\infty} <br />
in the following expression(F).

    F =  <br /> <br />
e^b \frac{\partial e^a}{\partial x}-e^a \frac{\partial e^b}{\partial x}<br />

    Where  e^a,e^b<br />
are given as follows:

    Infact they are the electric fields in two different waveguides a, b. However, The expressions are similar .

     e^a = s^a [ cos(\sigma^a x) + \frac {\kappa^a T^a} {\sigma^a} sin(\sigma^a x) ]<br />

     e^b = s^b [ cos(\sigma^b x) + \frac {\kappa^b T^b} {\sigma^b} sin(\sigma^b x) ]<br />

    I need to use the following representation of the Dirac delta function;

     \delta( \sigma ) = \lim_{x\to\infty} \frac {\sin(\sigma x)} {\pi \sigma}<br />

    Now, I need to show that the function F, after the limit applied is equal to :

    <br /> <br />
\lim_{x\to\infty}<br />
 F = (\sigma^{b^2}-\sigma^{a^2}) \frac {S^a S^b \pi}{2} (1 + \frac{\kappa^a T^a \kappa^b T^b}{\sigma^a \sigma^b}) \delta (\sigma^a - \sigma^b)<br /> <br />


    Please I need help to get this done. I would be grateful for the help.
    Last edited by kurapati; July 15th 2009 at 09:24 AM. Reason: gramatical mistake
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  2. #2
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    Jul 2009
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    Hi friends,

    I got the solution.
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