# Abel's Theorem

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## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Abel's Theorem** may refer to:

### 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.

This article is complete as far as it goes, but it could do with expansion.In particular: other theorems with the same name as they appear in our field of visionYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Expand}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Source of Name

This entry was named for Niels Henrik Abel.

## Historical Note

Abel's Theorem first appears in Abel's paper *Mémoire sur une Propriété Générale d'une Classe Très-Étendue de Fonctions Transcendantes*.

Carl Gustav Jacob Jacobi remarked that it was the greatest discovery in integral calculus in the $19$th century.

This article, or a section of it, needs explaining.In particular: It is not certain which of the various Abel's Theorems are being described in Calculus Gems.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |