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math.CA2010★ 3 cited
How to Add a Noninteger Number of Terms: From Axioms to New Identities
Markus Mueller, Dierk Schleicher
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 gener…
math.CA2005★ 2 cited
Fractional Sums and Euler-like Identities
Markus Mueller, Dierk Schleicher
We introduce a natural definition for sums of the form \[ \sum_{ν=1}^x f(ν) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory in…