1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bessel function problem

  1. Jun 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that:

    2. Relevant equations

    I know that

    3. The attempt at a solution

    I tried to calculate the integral and i get :
    [tex]\sum_{s=0}^{\infty}\frac{(-1)^sx^{2s+1}}{s!s!2^{2s}(2s+1)} [/tex]
    I dont see how I can arrive to the reuslt, if I calclate :
    [tex]\sum_{n=0}^{\infty}J_{2n+1}(x)=\sum_{s,n=0}^{\infty}\frac{(-1)^sx^{2s+2n+1}}{s!(s+2n+1)!2^{2n+2s+1}} [/tex]
    I tried to arrive to the same result, but I cant, shall I use Legendre's duplicantion formula?
    But even if I use it I don't think that's the way
    Thank you!
    Last edited: Jun 5, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?

Similar Discussions: Bessel function problem
  1. Hyperbolic functions (Replies: 0)

  2. Generating Functions (Replies: 0)