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October 23rd, 2009, 04:23 AM  #1 
Newbie Joined: Oct 2009 Posts: 2 Thanks: 0  Solving arctan( k * x ) + x = c
Hello everybody Sorry if this is the wrong forum, but I thought it might be applicable here since I have a feeling complex analysis is needed. I am working on a solution, where I'm currently stuck with an equation of the following form. arctan( k * x ) + x = c x is real and positive, and can even be above zero if this helps the solution. k and c are real I need to solve this equation with respect to x. So far I can't seem to solve it, and series expansion is not usefull because my x can be larger than 1. If a very nice expression can be formed using x > 0 and x < 1, then I might be able to fix this by scaling the expression. Any help would be appreciated. /Henrik Andresen 
October 23rd, 2009, 07:30 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,844 Thanks: 1566 
Either find separate series solutions for kx < 1 and kx > 1 or solve by successive approximation.

October 26th, 2009, 12:22 AM  #3 
Newbie Joined: Oct 2009 Posts: 2 Thanks: 0  Re: Solving arctan( k * x ) + x = c
Hey Thank you for the reply. Is it not possible to solve exact? The constant 'k' has to be isolated and is in fact a placeholder for the expression 'tan( theta/2 + pi/4)', where I in the end has to find theta. /Henrik 

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