Is it possible?

• To: mathgroup at smc.vnet.net
• Subject: [mg33775] Is it possible?
• From: Zekeriya Muslu <zekeriya at netas.com.tr>
• Date: Tue, 16 Apr 2002 03:50:23 -0400 (EDT)
• Organization: Nortel
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Dear News-Group,

I am beginner to mathematica, I have learned to use Bessel
and Hankel functions,
but still I could not solved my following equation:

J1(x): first kind Bessel Function,  1. order
J0(x): first kind Bessel function,  0. order
H1(x): second kind Hankel function, 1. order
H0(x): second kind Hankel function, 0. order

kt1 = sqrt(w mu1(w epsilon1 - j sigma1) + gamma^2)
kt2 = sqrt(w mu2(w epsilon2 - j sigma2) + gamma^2)

Known Parameters:   mu1, mu2, epsilon1, epsilon2, sigma1, sigma2, r0,
omega
Unknown Parameter:  only gamma

the difficult equation is follows:

J1(kt1  r0)  (j omega epsilon1 + sigma1)     H1(kt2  r0)  (j omega epsilon2 + sigma2)
-----------   --------------------------  =  ----------- ---------------------------
J0(kt1  ro)      kt1  r0                     H0(kt2 r0)         kt2  r0

This is my equation containing different order Bessel and Hankel
functions that uses kt1 and kt2 which are function of gamma.

I think this is very difficult equation to solve.
Is it possible to solve it by using mathematica?
I couldn't build any alghoritm.  Could you help me please?

Best regards,
zekeriya.

```

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