Author 
Comment/Response 
Nigel Eames

10/19/99 11:20am
I really would appreciate your help in solving this integral and if it's possible show the solution step by step.
I wonder if the integral could be plotted, in order to find a simpler function that closely approximates the given function. The integral is a function of z` and z (butI wanted to hold z constant at first).
E=[1+ (1/k^2)(2nd parital diff eq respect to z)]{2 Integral{sin[k(Lz`)] * Exp {jkSqrt[(zz`)^2 + a^2]} / Sqrt[(zz`)^2 + a^2]}dz`}
The limits are from 0 to L.
where,
z = L/2 (a try)
lamda = 3 meters
L = lamda/4 = 0.75 meters
a = 0.03 meters
k = 2 Pi/lamda
E = Electric field in the gap
I split the integral into the real and imaginary parts. I attempted to integral the imaginary part first.
I used Taylor series to approximate the function for L=0.4. It turns out that a fourth order expansion is a good approximation. Mathematica was able to integral it. It seems unable to differentiate the integral and add to it the original integral. I would really appreciate your help with this difficult problem.
I have a copy of Mathematica for students version 3.0.0, license: L27091961, running on a Pentium 333MHz with a Windows 98 OS.
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