```Date: May 8, 2013 7:49 PM
Author: Nasser Abbasi
Subject: Re: how find a relation between unknowns in this equation?please<br> help me

On 5/8/2013 4:41 PM, ghasem wrote:> "ghasem " <shaban_sadeghi@yahoo.com> wrote in message <kmeg52\$jkt\$1@newscl01ah.mathworks.com>...>> Hi.>> I have a non-linear equation including bessel functions with complex argument,as following:>>>> my_equation=(w*sqrt(k^2-100)*besseli(1,sqrt(k^2- w))*besselk(0,sqrt(k^2-100))+...>>                                             besselk(1,sqrt(k^2-100))*besseli(0,sqrt(k^2- w)));> ==============> I'm sorry,I forgot that tell above equation is =0.i.e:> I have equation of  f(real(k),imag(k),w)=0;  % f = my_equation> that:> my_equation=(w*sqrt(k^2-100)*besseli(1,sqrt(k^2- w))*besselk(0,sqrt(k^2-100))+...>                                              besselk(1,sqrt(k^2-100))*besseli(0,sqrt(k^2- w))) =0> please direct me...> thanks> ghasem>I guess you have 4 options to solve your bessel functionequation.1) solve the real and the imaging parts as was talked about beforeand combine result.2) use symbolic solve():w=99; syms k;my_equation=(w*sqrt(k^2-100)*besseli(1,sqrt(k^2- w))*besselk(0,sqrt(k^2-100))+...           besselk(1,sqrt(k^2-100))*besseli(0,sqrt(k^2- w)));solve(my_equation,k)  - 0.00023072214491381421450643003838304 - 2.1259310417079225152113020224253*i3) Use a computer algebra system that supports root finding withcomplex numbers:----------------------------Clear[a, b, k];w = 99;r = Sqrt[k^2 - 100];eq = w r BesselI[1, r] BesselK[0, r] + BesselK[1, r] BesselI[0, r];FindRoot[eq == 0, {k, 0.01 + 2 I}]{k -> 0.000263968 + 1.87608 I}FindRoot[eq == 0, {k, 0.01 + 2 I}]FindRoot[eq == 0, {k, 100}]{k -> 7.1247 + 0.000100538 I}FindRoot[eq == 0, {k, 99 + 200 I}]{k -> 9.99814 + 0.0014217 I}-------------------------4) use a matlab toolbox that allows complex root findingsuch as Chebfun and others like it. You can search fileexchangeon this topic.good luck,--Nasser
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