Indicial Equation for Legendre's Eq. at x=1,-1

[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

 

[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]<br /> what are y&#039; and y&quot;? What do you get when you put those into the equation?<br /> Assuming a_0 is not 0, what is the coefficient of the lowest power of x in that equation?

 

[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.

 

[sonia akram]

HallsofIvy, that's 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?

 

[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
y= \sum_{n=0}^\infty a_n (x- x_0)^{n+ c}

 

[sonia akram]

thx a lot for ur help!