Mathematica help

*To*: mathgroup at smc.vnet.net*Subject*: [mg20314] Mathematica help*From*: Niguel Eames <Neames at ITA.CI.LA.CA.US>*Date*: Fri, 15 Oct 1999 20:20:43 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Mathgroup, I need help to resolve 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 (but a wanted to hold z constant at first). E=[1+ (1/k^2)(2nd parital diff eq respect to z)]{2 Integral{sin[k(L-z`)] * Exp {jkSqrt[(z-z`)^2 + a^2]} / Sqrt[(z-z`)^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: L2709-1961, running on a Pentium 333MHz with a Windows 98 OS.

**Local Variables**

**error function**

**Re: Local Variables**

**error function**