Proving the Relation for the First Kind Bessel Function: My Scientific Discovery

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prove the relation for the Bessel function of first kind
 

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have you started to attempt to do this?
if so show us how far you got
 
genericusrnme said:
have you started to attempt to do this?
if so show us how far you got

Is this ok? What shoud I do with integral and summ? Don't have an idea.
How to solve that integral?
 

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I did it.
 
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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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