Thread: Convergent power series of (x^2)-(c^2)?

1. Convergent power series of (x^2)-(c^2)?

Hi,
I'm basically trying to understand why x=0 is a regular singular point of bessels equation order c.

I get up to:
x^2*q(x)= (x^2-c^2)
but my lecturer said you must show it as a convergent power series.
I can take a limit of x-->0 thus showing its analytic but I can't obtain the series.

Any help appreciated

2. Originally Posted by Roland25
Hi,
I'm basically trying to understand why x=0 is a regular singular point of bessels equation order c.

I get up to:
x^2*q(x)= (x^2-c^2)
but my lecturer said you must show it as a convergent power series.
Show [b]what[b] "as a convergent power series"? $x^2- c^2$ is itself a trivially "convergent" power series since all coefficients of powers above 2 are 0.

I can take a limit of x-->0 thus showing its analytic but I can't obtain the series.

Any help appreciated