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arXiv · 2105.04592

Telescopic, Multiplicative, and Rational Extensions of Summations

Robert Dawson·Grant Molnar
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Abstract

A summation is a shift-invariant ${\rm R}$-module homomorphism from a submodule of ${\rm R}[[\sigma]]$ to ${\rm R}$ or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we revisit telescoping, we study multiplicative closures of summations (such as the usual summation on convergent series) that are not themselves multiplicatively closed, and we study rational extensions as a generalization of telescoping.

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Robert Dawson, Grant Molnar. 2021-05-10. Telescopic, Multiplicative, and Rational Extensions of Summations. https://arxiv.org/abs/2105.04592

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