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F
Lv 6
F asked in Science & MathematicsMathematics · 1 decade ago

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

Relevance
  • ?
    Lv 6
    1 decade ago
    Favorite 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

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