An Extension of the Euler‐Maclaurin Summation Formula to Functions with a Branch Singularity
An Extension of the Euler‐Maclaurin Summation Formula to Functions with a Branch Singularity
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DOI：
10.1002/sapm1961401271
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发表时间：
1961-04
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影响因子：
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通讯作者：
I. Navot
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文献类型：
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作者：
I. Navot
(1) 其中 n 和 m 是任意正整数，f (x) 是任意实连续函数，在 0~ x~ 1 处具有高达 2m 阶的连续导数。 a 通常受 0< a~ 1 的限制，但最重要的两个实际情况是 a=！ a= 1. B~(a) 是伯努利 Jl 次多项式 R2m 是下式给出的余数
(1) where nand m are arbitrary positive integers and f (x) is an arbitrary real continuous function, with continuous derivatives up to the order 2m, at 0~ x~ 1. a is generally restricted by 0< a~ 1 but the two most important practical cases are a=! and a= 1. B~(a) is Bernoulli's polynomial of degree Jl R2m is the remainder given by