- #1
Kopernikus89
- 2
- 0
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 :-)
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 :-)