Synthesizing Sums

Details Synthesizing Sums Synthesizing Sums

2007-02-21

arxiv.org/abs/math/0702605v1

Mathematics

General Mathematics

Scientific paper

Polynomial functions $f : \mathbb{N}_+ \longrightarrow \mathbb{N}_+$ are studied for which sums of arbitrary length $f (1) + f (2) + f (3) + >... + f (n)$, with $n \in \mathbb{N}_+$, can be expressed by polynomial functions $g : \mathbb{N}_+ \longrightarrow \mathbb{N}_+$ which involve a bounded number of operations, thus not depending on $n$. Open problems and extensions are presented.

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