Abel's Limit Theorem

Theorem

Let $\sequence {a_i}$ be a convergent series.

The limit which is assigned by the Abel summation method exists and equals the sum of the series.

Proof

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Also see

• Cesàro Summation

Source of Name

This entry was named for Niels Henrik Abel.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Abel's limit theorem
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Abel's Limit Theorem