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October 23rd, 2009, 04:23 AM   #1
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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
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October 23rd, 2009, 07:30 PM   #2
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Either find separate series solutions for kx < 1 and kx > 1 or solve by successive approximation.
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October 26th, 2009, 12:22 AM   #3
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Re: Solving arctan( k * x ) + x = c


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.

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