On the Sums

The Sums S(n) continue to attract considerable interest in mathematical disciplines ranging from Fourier analysis to number theory. Elkies presents Calabi's proof, which uses only the formula for change of variables of multiple integrals. He also relate S(n) and polytope volumes to the enumerat...

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Bibliographic Details
Published in:The American mathematical monthly 2003-08, Vol.110 (7), p.561-573
Main Author: Elkies, Noam D.
Format: Article
Language:English
Subjects:
Mathematical analysis
Mathematics
Number Concepts
Numbers
Theory
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Summary:The Sums S(n) continue to attract considerable interest in mathematical disciplines ranging from Fourier analysis to number theory. Elkies presents Calabi's proof, which uses only the formula for change of variables of multiple integrals. He also relate S(n) and polytope volumes to the enumeration of alternating and cyclically alternating permutations.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2003.11919997