elimination of a real variable from a complex function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75428] elimination of a real variable from a complex function*From*: "Gautam Sethia" <gautam.sethia at gmail.com>*Date*: Mon, 30 Apr 2007 03:39:18 -0400 (EDT)

hi.. I am doing the stability analysis of the solutions of a complex integral equation. In this context I am facing a problem which is detailed below. Could some body help me resolve the problem. Thanks Gautam C Sethia *************************************** The following complex integral equation is in a single real variable \[Lambda] and a number of real parameters viz. A, \[CapitalOmega], v, \[Alpha], k and n. The last two parameters i.e. k and n can have only integer values. My objective is to eliminate \[Lambda] from this equation and have an equation only in terms of the parameters. This should in principle be possible as the complex equation can be reduced to a system of two real equations and a single real variable \[Lambda] and that should enable us to eliminate \[Lambda] from these two equations. \[ImaginaryI]\[Lambda] + Integrate[((A*Cos[z] + 1)*Cos*(k*z + \[Alpha] + (\[CapitalOmega]*Abs[z])/v)* (1 - E^((-I)*(n + (\[Lambda]*Abs[z])/v))))/(2*Pi), {z, -Pi, Pi}] = 0 I tried the following: 1. I wrote the above equation as a set of two equations by separating into real and imaginary parts. That is facilitated by the fact that variable \[Lambda] as well as all other parameters are real. 2. In each of these two equations, the integration could be done separately from -\[Pi] to 0 and 0 to \[Pi] so that we can get rid of the Abs function on z. 3. The right hand side of these two equations can then be integrated in mathematica (it takes about 10-15 minutes on my laptop) giving horrendous looking analytical expressions. 4. I am at a loss at this point and have no clue how to eliminate \[Lambda] from these two equations involving those two expressions. Could you please suggest me a way to go about achieving my objective using mathematica. Thanks...Gautam C Sethia