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Problem with Frobenius?
Hi.
I am looking at a working in a book and there is a step I don´t understand, I need some help with what happens.
Here is the original problem:
6x^2y´´ + 7xy´ - (1+x^2)y = 0 ;
Then there are a number of steps shown which I understand until:
1) Sum (from 0 to infinity) (6(n+r)(n+r-1) + 7(n+r) -1) subscript (a) x^n+r - sum (from 2 to infinity) a sub (m-2) * x^m+r = 0
2) Sum (from 0 to infinity) (6(n+r)^2 + n + r - 1) a (sub n) - a (sub n-2)) * x^n+r = 0
I don´t understand how to get from 1 to 2. 1 I understand but not how to get from 1 to 2. Where is the 7 in 2?
Please explain that and what happens.
Thank you.
1 Answer
- ?Lv 61 decade agoFavorite Answer
6(n+r)(n+r-1) + 7(n+r) -1
=6(n+r)^2 - 6(n+r) +7(n+r) -1
=6(n+r)^2 +(n+r) -1