# Series solutions near a regular singular point

1. Apr 16, 2008

### phrankle

For solving a series solution near a regular singular point with the Frobenius method, why is it that the indices of summation derivatives aren't shifted?

For example, in my textbook and lecture notes

y = $$\sum$$A$$_{}n$$x$$^{}n+r$$ from n=0 to infinity

y' = $$\sum$$(n+r)A$$_{}n$$x$$^{}n+r-1$$ from n=0 to infinity

y'' = $$\sum$$(n+r)(n+r-1)A$$_{}n$$x$$^{}n+r-2$$ from n=0 to infinity

But shouldn't the index for y' be from n=1 to infinity because it shifts up when you take the derivative of a summation? Shouldn't the index for y'' be from n=2 to infinity?

Thanks.

2. Apr 16, 2008

### tiny-tim

Welcome to PF!

Hi phrankle! Welcome to PF!