Definition:Harmonic Series/General

This page is about general harmonic series. For other uses, see harmonic.

Definition

Let $\sequence {x_n}$ be a sequence of numbers such that $\sequence {\size {x_n} }$ is a harmonic sequence.

Then the series defined as:

$\ds \sum_{n \mathop = 1}^\infty x_n$

is a (general) harmonic series.

Also see

• Results about harmonic series (particular and general) can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): harmonic series: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): harmonic series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): harmonic series
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): harmonic series
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): harmonic series