# Simple indicial eq

1. Nov 17, 2008

### sonia akram

what is the indicial equation associated with regular singularities x=1 and x=-1 of legendre's eq.?
(1-x^2)y''-2xy'+a(a+1)y=0

2. Nov 17, 2008

### HallsofIvy

What have you done to try to find it yourself?

If you write
$$y= \sum_{n=0}^\infty a_n x^{n+c}[/itex] what are y' and y"? What do you get when you put those into the equation? Assuming a_0 is not 0, what is the coefficient of the lowest power of x in that equation? 3. Nov 17, 2008 ### matematikawan Don't they have a general formula for indicial equation for the Legendre's equation. I remember they have such a formula for Euler-Cauchy differential equation. 4. Nov 18, 2008 ### sonia akram HallsofIvy, thats the series solution for singularity x=0, if we are esprcially working for singularity x=1 or -1 than indicial would be different or not? 5. Nov 18, 2008 ### HallsofIvy Yes, I was using the most common application as an example. If a differential equation has a singularity at x= x0 you would use [tex]y= \sum_{n=0}^\infty a_n (x- x_0)^{n+ c}$$

Last edited by a moderator: Nov 23, 2008
6. Nov 23, 2008

### sonia akram

thx a lot for ur help!