# Thread: Bessel Equation generl solution

1. ## Bessel Equation generl solution

Hello everyone!

What's the general "2 series" solution of bessels equation?

Is it $\displaystyle c_0J_{\nu} + c_1J_{-\nu}$ or is it $\displaystyle c_0J_{\nu} + c_1Y_{\nu}$?
And why?

2. If $\displaystyle \nu$ is non integer $\displaystyle J_{\nu}$ and $\displaystyle J_{-\nu}$ are independent so that the solution is $\displaystyle y=c_{1} J_{\nu} + c_{2} J_{-\nu}$. If $\displaystyle \nu$ is integer the problem is a little more complicated and requires a little more time...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. If is integer the problem is a little more complicated and requires a little more time...
Aaah... So you mean that if $\displaystyle \nu$ is an integer the general solution for the equation is $\displaystyle y=c_0J_{\nu}+c_1Y_{\nu}$ because $\displaystyle J_{\nu}$ and $\displaystyle J_{-\nu}$ are linerearily dependent. Right?

4. Yes!!!...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$