Linear dependence of bessel equation

[asdf1]

why for bessel equations, if n isn't an integer, you can have the solution
y(x)=(c1)Jn(x) +(c2)J(-n)x
but isn't true if n's an integer?

 

[HallsofIvy]

Same answer as to your other question. J_n and J_-n are not independent precisely because J_-n= (-1)ⁿJ_n.

http://www.ucl.ac.uk/~ucahdrb/MATHM242/LegBess.pdf

 

[asdf1]

thank you!