Simple integration of bessel functions

Mappe
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I seek a way to integrate J0, bessel function. I try to use some of the identities I can find, but it takes me no were. Please help!
 
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The simple integral of an integer order Bessel function is given by Struve functions. You can find them in ch. 11 , "Integrals of Bessel Functions" of Abramowitz and Stegun. If you are serious about math, buy a copy (the Dover edition is inexpensive). For now you can browse an old online copy here
http://www.convertit.com/Go/Convertit/Reference/AMS55.ASP"
 
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Have a look at

http://www.fh-jena.de/~rsh/Forschung/Stoer/besint.pdf
 
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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