On a Class of Conditionally Convergent Infinite Products

Compactification of a set of matrices with convergent infinite products

We generalize and unify some aspects of the work of I. Daubechies, J.C. Lagarias [Linear Algebra Appl. 162 (1992) 227–263] on a set R of matrices with right-convergent-products (RCPs). We show that most properties of an RCP set R pass on to its compactification R (i.e., its closure in the matrix space). Results on finite RCP sets generally hold for compact RCP sets, among which is the existence...

On rearrangements of conditionally convergent series

Rearrangement of a Conditionally Convergent Series

One of the surprising results in an elementary calculus course is that a rearrangement of a conditionaly convergent series may change its sum, even its very convergence. Observing typical textbook examples of this phenomenon, it turns out that during the rearrangement some of the terms are moved arbitrarily large distances from their original locations. Is this necessary? The answer is positive...

A Distributional Approach to Conditionally Convergent Series

Whether the car’s gas tank is filled up on Monday and the paycheck is deposited on Tuesday, or vice versa, the contribution of those two transactions to the checkbook’s final balance is the same. By the commutative property, order does not matter for the algebraic addition of a finite number of terms. However, for a super banker who conducts an infinite number of transactions, order may matter....

On Faster Convergent Infinite Series

Recommended by Laszlo Toth Suffcient conditions, necessary conditions for faster convergent infinite series, faster τ-convergent infinite series are studied. The faster convergence of infinite series of Kummer's type is proved. Copyright q 2008 Dušan Hoí y et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distributi...