Heaviside's Method for Regular Singular Points

[Ted123]

[PLAIN]http://img820.imageshack.us/img820/9868/heaviside.png

 

[HallsofIvy]

You should have y''+ py'+ qy= 0 and (x- x_0)^2q(x) finite. You have left out the "q"s. Also, you say that x_0 is a regular singular point if those are finite. In order that x_0 be a singular point, at least one of the two limits of p and q, as x goes to x_0 must not exist.

Yes, from what you have, x= 0 is a regular singular point for a and c, it not a regular singular point for d. But I would say that x= 0 is not even a singular point for b.

 

[Ted123]

You should have y''+ py'+ qy= 0 and (x- x_0)^2q(x) finite. You have left out the "q"s. Also, you say that x_0 is a regular singular point if those are finite. In order that x_0 be a singular point, at least one of the two limits of p and q, as x goes to x_0 must not exist.

Yes, from what you have, x= 0 is a regular singular point for a and c, it not a regular singular point for d. But I would say that x= 0 is not even a singular point for b.

Yes, I accidently missed the q's. And thanks for the explanation. I think the definition should read 'A singular point x_0 is called regular if both those are finite as x-> x_0.'