Alternate Sylvester sums on the Frobenius set

作者：Wang Weiping^*; Wang Tianming

来源：Computers & Mathematics with Applications, 2008, 56(5): 1328-1334.

DOI：10.1016/j.camwa.2008.02.031

• alternate sylvester sums
• Frobenius problem
• sums of powers of integers
• Bernoulli polynomials
• Euler polynomials
• combinatorial identities

The alternate Sylvester sums are T-m(a, b) = Sigma(n epsilon 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.

• 出版日期2008-9
• 单位大连理工大学