Bessel’s equation: x^2 (d^2y/dx^2) + x(dy/dx) + (x^2 - a^2)y = 0

[hosseinmath]

Bessel’s equation: x^2 (d^2y/dx^2) + x(dy/dx) + (x^2 - a^2)y = 0

hello my friends

my question is urgent please help

how can i derive

from properties of bessel function



















J0(0) Jν(x) J−n(x) ddx

x−νJν(x)

ddx

xνJν(x)

ddx

Jν(x)

xJν+1(x) ∫x−νJν+1(x)dx ∫xνJν−1(x)dx =1

=0(if ν

0), =(−1)nJn(x)

=−x−νJν+1(x)

=xνJν−1(x)

=21

Jν−1(x)−Jν+1(x)

=2νJν(x)−xJν−1(x)

=−x−νJν(x)+C

=xνJν(x)+C

(10.31) (10.32) (10.33) (10.34) (
(

 

[HallsofIvy]

What specific properties of the Bessel functions are you referring to?