Abel's test, also called Abel's criterion, is a method for testing the convergence of an infinite series, named after the mathematician Niels Henrik Abel, who proved it in 1826. Two slightly different versions exist, one used with series of real numbers and the other with power series in complex analysis, and a related form, Abel's uniform convergence test, gives a criterion for the uniform convergence of a series of functions that depend on parameters.
Facts
StatementIf the series sum of a_n converges and b_n is a monotone bounded sequence, then the series sum of a_n b_n also converges. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Abel's test, Wikipedia
Named After
Proved By
Source Abel's test, Wikipedia
Sources
1. Abel's test, Wikipedia
Lead section
The test is named after mathematician Niels Henrik Abel, who proved it in 1826.
Historical statement
The test is named after mathematician Niels Henrik Abel, who proved it in 1826.
Proved By: Niels Henrik Abel, Lead
The test is named after mathematician Niels Henrik Abel, who proved it in 1826.
In Branch: Complex Analysis, Lead paragraph
There are two slightly different versions of Abel's test, one is used with series of real numbers, and the other is used with power series in complex analysis.
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