- #1
phrankle
- 6
- 0
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 = \sumA_{}nx^{}n+r from n=0 to infinity
y' = \sum(n+r)A_{}nx^{}n+r-1 from n=0 to infinity
y'' = \sum(n+r)(n+r-1)A_{}nx^{}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.
For example, in my textbook and lecture notes
y = \sumA_{}nx^{}n+r from n=0 to infinity
y' = \sum(n+r)A_{}nx^{}n+r-1 from n=0 to infinity
y'' = \sum(n+r)(n+r-1)A_{}nx^{}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.
