My Math Forum Series of Bessel functions

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 December 15th, 2015, 05:19 AM #1 Newbie   Joined: Dec 2015 From: Russia, Moscow Posts: 1 Thanks: 0 Series of Bessel functions Hello! I stuck with my physics problem. I have a solution in the form of $\displaystyle \sum_{n=0}^{\infty }\frac{J_n(x)}{H_n(x)}$, where x is grate than 1 but fixed, thus it's not possible to use asymptotic form for Bessel functions with large or small x. However, I made some numeric calculations and found that terms of series start to decrease very quickly if n > x, so it's sufficient to take only first [x] terms. Another point is that I know the answer (from physical sense and also from numeric calculations), and the answer is approximately x/2. I need help to obtain the answer by direct calculation this series. Any suggestions?

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