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有限三角和的表示

发布时间:2019-05-27 14:30
【摘要】:本文利用Cauchy留数定理和生成函数,证明了许多有限三角和为有理数,即用高阶Bernoulli多项式和高阶Euler多项式来表示有限三角和.特别,我们也得到了有限三角和的一些有趣的互反公式.具体地说,一、首先,设n为大于2的偶数,k为正整数,r为非负整数且r≤礼-1,Cvijovic得到我们推广的结果为:(1)定理3.1设n为大于1的奇数,k,r为非负整数且r≤n-1/2,那么(2)定理3.11设n为大于2的偶数,k,r为正整数且r≤n/2,则二、其次,设m,礼为互素的正整数且m+n=μc,其中μ和c为正整数,Berndt和Yeap得到我们推广的结果为:(1)定理3.15设m,礼为大于2的奇数且(m,礼)=1,那么(2)定理3.16设m,n为大于2的奇数且(m,礼)=1,那么
[Abstract]:In this paper, by using Cauchy residue theorem and generating function, it is proved that many finite trigonometric sums are rational numbers, that is, the finite trigonometric sums are represented by higher-order Bernoulli Polynomials and higher-order Euler Polynomials. In particular, we also get some interesting inverse formulas for finite trigonometric sums. Specifically, first, let n be an even number greater than 2, k be a positive integer, r be a nonnegative integer and r 鈮,

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