Category:Abel's Theorem

This category contains pages concerning Abel's Theorem:

Abel's Limit Theorem

Let $\ds \sum_{k \mathop = 0}^\infty a_k$ be a convergent series in $\R$.

Then:

$\ds \lim_{x \mathop \to 1^-} \paren {\sum_{k \mathop = 0}^\infty a_k x^k} = \sum_{k \mathop = 0}^\infty a_k$

where $\ds \lim_{x \mathop \to 1^-}$ denotes the limit from the left.

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Source of Name

This entry was named for Niels Henrik Abel.