Frobenius集合上的加权Sylvester和

T. Komatsu, Yuancao Zhang
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引用次数: 19

摘要

设$a$和$b$为相对素数正整数。本文用apostoll - bernoulli数显式给出了加权和$\sum_{n\in{\rm NR}(a,b)}\lambda^{n-1}n^m$,其中$m$为非负整数,${\rm NR}(a,b)$为不可用$a$和$b$表示的正整数集合。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Weighted Sylvester sums on the Frobenius set
Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\sum_{n\in{\rm NR}(a,b)}\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.
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