Bessel function

  • #1
Hello
I have the following problem:
I must show that the Bessel function of order [tex]n\in Z [/tex]

[tex]J_n(x)=\int_{-\pi}^\pi e^{ix\sin\vartheta}e^{-in\vartheta}\mathrm{d}\vartheta [/tex]

is a solution of the Bessel differential equation

[tex]x^2\frac{d^2f}{dx^2}+x\frac{df}{dx}+(x^2-n^2)f=0[/tex]

Would be very thankful for some help :-)
 

Answers and Replies

  • #3
well the first 2 summands equal 0 (i hope i've calculated this correctly) but its more a problem with the third one. how can i show that this will also become 0?
 
  • #4
607
0
Let's call your right-hand-side [itex]F(x)[/itex]
Then: what do you get for [itex]F'(x)[/itex] and [itex]F''(x)[/itex]
 
  • #5
1
0
Hello,
I'd like to know how to solve the ODE shown in the attached file using Bessel functions

I will be very grateful!!
 

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