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Alternate Sylvester sums on the Frobenius set

✍ Scribed by Weiping Wang; Tianming Wang

Book ID
104008228
Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
267 KB
Volume
56
Category
Article
ISSN
0898-1221

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✦ Synopsis

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The alternate Sylvester sums are T m (a, b) = n∈NR (-1) n n m , where a and b are coprime, positive integers, and NR is the Frobenius set associated with a and b. In this note, we study the generating functions, recurrences and explicit expressions of the alternate Sylvester sums. It can be found that the results are closely related to the Bernoulli polynomials, the Euler polynomials, and the (alternate) power sums over the natural numbers.

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