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- W2331554867 abstract "Let Σa k be an infinite series of real numbers and let π be a permutation of N , the set of positive integers. The series Σa π(k) is then called a rearrangement of Σa k . A classical theorem of Riemann states that if Σa k is a conditionally convergent series and s is any fixed real number (or ± ∞), then there is a permuation π such that Σa π(k) = s. The problem of determining those permutations that convert any conditionally convergent series into a convergent rearrangement (such permuations are called convergence preserving) has received wide attention (see, for example [ 6 ]). Of special interest is a paper by P. A. B. Pleasants [5] in which is shown that the set of convergence preserving permutations do not form a group. In this paper we consider questions similar to those above, but for rearrangements of divergent series of positive terms. We establish some notation before stating the precise problem." @default.
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- W2331554867 date "1982-08-01" @default.
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- W2331554867 title "Rearrangements that Preserve Rates of Divergence" @default.
- W2331554867 doi "https://doi.org/10.4153/cjm-1982-064-2" @default.
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