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arXiv · 2609.00687

A unification of Euler-Maclaurin and Euler-Boole summation formulas

Yuan He
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Abstract

In this paper, we establish a summation formula associated with the generalized Apostol-Bernoulli functions. This formula unifies the Euler-Maclaurin summation formula, the Euler-Boole summation formula, and the character analogues of these two formulas. We also apply it to obtain the general power sum formula and the special values of Berndt's generalized $L$-function at non-positive integers.

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Yuan He. 2026-09-01. A unification of Euler-Maclaurin and Euler-Boole summation formulas. https://arxiv.org/abs/2609.00687

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