Character analogues of the poisson and Euler-MacLaurin summation formulas with applications
Character analogues of the poisson and Euler-MacLaurin summation formulas with applications
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DOI：
10.1016/0022-314x(75)90045-1
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发表时间：
1975-11
影响因子：
0.7
通讯作者：
B. Berndt
中科院分区：
文献类型：
--
作者：
B. Berndt
推导了泊松和欧拉-麦克劳林求和公式的字符版本。现在出现的是广义伯努利数和多项式，而不是经典欧拉-麦克劳林公式中出现的伯努利数和多项式。给出了结果的许多应用。特别是，它应用于 L 函数的评估、Lipschitz 求和公式的字符类似物的推导以及经典伽马函数的新字符版本的检查。
Character versions of the Poisson and Euler-Maclaurin summation formulas are derived. Instead of Bernoulli numbers and polynomials which appear in the classical Euler-Maclaurin formula, generalized Bernoulli numbers and polynomials now appear. Many applications of the results are given. In particular, applications are made to the evaluation ofL-functions, the derivation of a character analogue of the Lipschitz summation formula, and the examination of a new character version of the classical gamma function.