Is There an Analytical Solution to the Transcendental Equation x = cot(x)?

twoflower
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Hi,

can somebody see if there is a way to solve this analytically?

<br /> x = \mbox{cotg } x<br />

I know it could be solved numerically, but I'm interested in analytical solution only (if it exists, of course).

Thank you very much.
 
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Sorry - none exist! :(
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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