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

@article{Mller2011HowTA,
  title={How to Add a Noninteger Number of Terms: From Axioms to New Identities},
  author={M. M{\"u}ller and D. Schleicher},
  journal={The American Mathematical Monthly},
  year={2011},
  volume={118},
  pages={136 - 152}
}
  • M. Müller, D. Schleicher
  • Published 2011
  • Mathematics, Computer Science
  • The American Mathematical Monthly
  • 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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