论文标题
cotangent总和的痕量方法
The Trace Method for Cotangent Sums
论文作者
论文摘要
本文介绍了Cotangent的整数力量总和的组合研究，这是古典微积分中的一个流行主题。我们的主要工具将cotangent值的实现为具有整数矩阵的简单自我伴组的特征值。我们使用跟踪方法得出有关总和的整数值的结论，并扩展生成函数以获得明确的评估。值得注意的是，在整个计算过程中，组合剂受到较高的切线和北极数的支配。最后，我们指出了在整数参数上的riemann zeta函数值的新近似值。
This paper presents a combinatorial study of sums of integer powers of the cotangent which is a popular theme in classical calculus. Our main tool the realization of cotangent values as eigenvalues of a simple self-adjoint matrix with integer matrix. We use the trace method to draw conclusions about integer values of the sums and expand generating functions to obtain explicit evaluations. It is remarkable that throughout the calculations the combinatorics are governed by the higher tangent and arctangent numbers exclusively. Finally we indicate a new approximation of the values of the Riemann zeta function at even integer arguments.
