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arXiv · 1001.4695

How to Add a Noninteger Number of Terms: From Axioms to New Identities

Markus Mueller·Dierk Schleicher
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Abstract

Starting from a small number of well-motivated axioms, we derive a unique definition of sums with a noninteger number of addends. These "fractional sums" have properties that generalize well-known classical sum identities in a natural way. We illustrate how fractional sums can be used to derive infinite sum and special functions identities; the corresponding proofs turn out to be particularly simple and intuitive.

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Markus Mueller, Dierk Schleicher. 2011-03-02. How to Add a Noninteger Number of Terms: From Axioms to New Identities. https://arxiv.org/abs/1001.4695

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