# Potential series method

1. Dec 19, 2012

### matematikuvol

Why sometimes we search solution of power series in the way:
$$y(x)=\sum^{\infty}_{n=0}a_nx^n$$
and sometimes
$$y(x)=\sum^{\infty}_{n=0}a_nx^{n+1}$$???

2. Dec 20, 2012

### tiny-tim

hi matematikuvol!
no particular reason …

sometimes one gives neater equations than the other …

they'll both work (provided, of course, that y(0) = 0)

3. Dec 21, 2012

### matematikuvol

I think that in the case when
$$\alpha(x)y''(x)+\beta(x)y'(x)+\gamma(x)y(x)=0$$
if $\alpha(0)=0$ you must work with $\sum^{\infty}_{n=0}a_nx^{n+k}$, but I'm not sure.

4. Dec 21, 2012

### tiny-tim

but that's the same as $\sum^{\infty}_{n=0}b_nx^n$ with $b_n = a_{n-k}$ for n ≥ k, and $b_n = 0$ otherwise