Bessel Function Summation: Jo(x+y)

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Homework Statement



Show that Jn(x+y) = ∑ Jr(x)Jn-r(y) ; where (Jn)= bessel function , ∑ varies from

(-to+)infinity for r

Jo(x+y) = Jo(x)Jo(y) +2 ∑ Jr(x)J-r(y) ∑ varies from (1 to infinity) for r

Homework Equations





The Attempt at a Solution



I have solved the first one using generating function but am not able to arivve at a sloution for 2nd .
 
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not even 1 reply , wats happening guys ?
 
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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