PreprintCC BY 4.0arXiv
A unification of Euler-Maclaurin and Euler-Boole summation formulas
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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BibTeX
@misc{he2026unification,
title = {{A unification of Euler-Maclaurin and Euler-Boole summation formulas}},
author = {Yuan He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00687},
eprint = {2609.00687},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00687},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A unification of Euler-Maclaurin and Euler-Boole summation formulas
AU - Yuan He
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00687
UR - https://arxiv.org/abs/2609.00687
AB - 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.
ER -