【摘要】：本文利用Cauchy留數(shù)定理和生成函數(shù),證明了許多有限三角和為有理數(shù),即用高階Bernoulli多項式和高階Euler多項式來表示有限三角和.特別,我們也得到了有限三角和的一些有趣的互反公式.具體地說,一、首先,設n為大于2的偶數(shù),k為正整數(shù),r為非負整數(shù)且r≤禮-1,Cvijovic得到我們推廣的結果為：(1)定理3.1設n為大于1的奇數(shù),k,r為非負整數(shù)且r≤n-1/2,那么(2)定理3.11設n為大于2的偶數(shù),k,r為正整數(shù)且r≤n/2,則二、其次,設m,禮為互素的正整數(shù)且m+n=μc,其中μ和c為正整數(shù),Berndt和Yeap得到我們推廣的結果為：(1)定理3.15設m,禮為大于2的奇數(shù)且(m,禮)=1,那么(2)定理3.16設m,n為大于2的奇數(shù)且(m,禮)=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，

本文編號：2486224