Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Showing That the Modified Bessel Function of the First Kind is a Solution

  1. Nov 22, 2008 #1
    Hello,

    I am in the process of showing that the modified Bessel function, I_v(x), is a solution to the modified Bessel equation,

    x^2*y''+x*y'-(x^2+v^2)*y=0

    I have differentiated the MBF twice and plugged it in to show that the left hand side is in fact 0.

    After a good amount of work, I've come to the following left hand side:

    [​IMG]

    Where sigma=v.


    Is that right? The math seems straight forward, and I only did one change of index that looks correct to me. I'm skeptical about the end result though.
     
  2. jcsd
  3. Nov 22, 2008 #2
    Sorry, the actual left hand side I have are those two terms inside the sum multiplied by (x/2)^2k+v.

    All inside the sum.
     
  4. Nov 25, 2008 #3
    Not sure either. But the second term is undefined when k=0 , i.e. (-1)! = Γ(0) is undefined. Or do we assume the second term to be zero?
     
  5. Nov 25, 2008 #4
    Thank you for the response.

    I just realized I made a mistake by changing the index, resulting in that denomintor. I eventually obtained a series that converged to 0.

    Thank you again.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Showing That the Modified Bessel Function of the First Kind is a Solution
Loading...