Conditionally convergent

Conditionally convergent refers to a series that converges, but not absolutely, meaning that the series is converging because each term cancels out some of the previous terms. A conditionally convergent series can be rearranged in such a way that it can either diverge or converge to any finite value. Additionally, the terms of a conditionally convergent series can be rearranged in such order that the sum of the new series becomes equal to any given value, or the rearrangement can result in a divergent series.From: CRC Standard Mathematical Tables and Formulas [2018], A Concise Handbook of Mathematics, Physics, and Engineering Sciences [2019], Ordinary Differential Equations [2019]

Series Solutions: Preliminaries (A Brief Review of Infinite Series, Power Series and a Little Complex Variables)

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Published in Kenneth B. Howell, Ordinary Differential Equations, 2019

Kenneth B. Howell

If a series converges but is not absolutely convergent, then it is converging because each term “cancels out” some of the previous terms, and the series is said to be conditionally convergent. Such a convergence is somewhat unstable and can be upset by, say, rearranging the terms of the series in a clever way. Because of this, we will much prefer series that converge absolutely.

A novel parallel frequent itemset mining algorithm for automatic enterprise

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Published in Enterprise Information Systems, 2023

Yimin Mao, Bin Wu, Qianhu Deng, Soroosh Mahmoodi, Zhigang Chen, Yeh-Cheng Chen

where and represent any number. From commutative law, it is known that any finite sum or product is unaltered by reordering its terms or factors. Although many systems hold commutativity, there are other systems where the commutativity of multiplication is invalid. For instance, scalar multiplication of two vectors is commutative (i.e. ), but vector multiplication is not (i.e. ). Therefore, the commutative law does not necessarily hold for multiplication of conditionally convergent series.

The stress field of an infinite set of discrete dislocations

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Published in Philosophical Magazine Letters, 2021

Sivasambu Mahesh, Shyam M. Keralavarma

A fast and simple numerical method is proposed to sum the conditionally convergent series representing the stress fields induced by a two-dimensional countably infinite set of edge dislocations. The method cancels away long range spurious stresses without explicitly evaluating them.

Conditionally convergent

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Series Solutions: Preliminaries (A Brief Review of Infinite Series, Power Series and a Little Complex Variables)

A novel parallel frequent itemset mining algorithm for automatic enterprise

The stress field of an infinite set of discrete dislocations