发表机构
School of Mathematics and Big Data, Neijiang Normal University（内江师范学院数学与大数据学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Berndt广义L函数，引入广义Apostol-Bernoulli多项式与函数并建立其性质，证明该L函数整数点值可通过上述函数显式计算。
AI 中文摘要
本文研究Berndt（1975）提出的广义L函数，引入广义Apostol-Bernoulli多项式与广义Apostol-Bernoulli函数，建立其若干性质，包括这些函数的傅里叶级数，证明Berndt广义L函数在整数点的值可通过广义Apostol-Bernoulli函数显式计算。
英文摘要
In this paper, we study the generalized $L$-function considered by Berndt (1975). We introduce the generalized Apostol-Bernoulli polynomials and the generalized Apostol-Bernoulli functions, and establish some properties for them, including the Fourier series for these functions. We show that the values of Berndt's generalized $L$-function at integers are explicitly evaluated in terms of the generalized Apostol-Bernoulli functions.
Comments21 pages
