Kempner和的模态展开
The modal expansion of Kempner sums
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中文总结 AI 辅助
本文延续作者先前工作，针对Kempner和的模态展开，专门补充了块Irwin和$I(b,w,k)$在$k=0$且$w$为多位块时的完整讨论，完善了该框架的覆盖范围。
中文摘要 AI 辅助
本文是作者先前论文《块计数约束调和和：谱展开与块定向Euler–Maclaurin》的延续。在那篇参考文献中，我们给出了块Irwin和$I(b,w,k)$（$k\geq1$）的模态展开。当$w$为单个数字时，$k=0$的情形已得到充分发展，但对于$w$为多位块时，仅以非常简短的结论摘要形式呈现。尽管该框架已在先前论文中完全阐述，但$k=0$的情形需要补充专门的独立讨论，本文即提供此讨论。
英文摘要
This is a continuation of the author's earlier paper Block-count constrained harmonic sums: spectral expansion and block-directed Euler--Maclaurin. We presented in that reference the modal expansion of block-Irwin sums $I(b,w,k)$ for $k\geq1$. The case $k=0$ was fully developed when $w$ is a single digit, but it was presented only as a very short result summary for $w$ a multi-digit block. Although the framework is already completely exposed in the earlier paper, the case $k=0$ requires adding a separate, dedicated discussion, which is provided here.
