I need to solve a bessel function which is part of a larger PDE.

Unfortunately I missed the class where we talked about it.

I've come to$$R''(r)+\frac{1}{r}R'(r)+(\lambda-\frac{n^2}{r^2})R(r)=0$$Which is the standard form of the bessel function divided r^2.What would the solution be, in the context of this being a smaller part of partial differential equation?

My notes say to let$$J(r)=R(\frac{r}{\sqrt{\lambda}})$$

Question

I need to solve a bessel function which is part of a larger PDE. 

Unfortunately I missed the class where we talked about it.

I've come to$$R''(r)+\frac{1}{r}R'(r)+(\lambda-\frac{n^2}{r^2})R(r)=0$$Which is the standard form of the bessel function divided r^2.What would the solution be, in the context of this being a smaller part of partial differential equation?

My notes say to let$$J(r)=R(\frac{r}{\sqrt{\lambda}})$$

experimentx · Answer

Probably http://en.wikipedia.org/wiki/Bessel_function#Bessel_functions_of_the_first_kind_:_J.CE.B1