How can I adjust the index in summation notation for the Frobenius method?

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The discussion focuses on adjusting the index in summation notation for the Frobenius method, specifically the expression \sum_{k=0}^{\infty}a_{k}(k+r)(k+r-1)x^{k-1}. The user aims to transform the x term to the form x^n by setting n = k-1, but encounters an issue with the index starting at n = -1, which is deemed nonsensical in this context. The conversation emphasizes the importance of maintaining valid indices in mathematical expressions, particularly when applying the Frobenius method.

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\sum_{k=0}^{\infty}a_{k}(k+r)(k+r-1)x^{k-1}

I need to get my x term to look like xn.

If I set n = k-1, then that makes my index start at n = -1, which is silly. What can I do?
 
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Why is that silly? When k = 0, you have x^-1 in your original summation.
 
It doesn't make sense when I'm using it in the Frobenius method.
 
Last edited:

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