关于一些三角函数级数的封闭形式

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-16 DOI:arxiv-2407.12885

Slobodan B. Tričković, Miomir S. Stanković

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引用次数: 0

摘要

我们推导出了正弦或余弦函数上的三角级数的替代闭式公式，当用正整数立即替换分母中出现的参数时，会产生ingularity。通过应用 Choi-Srivastava 定理，我们将三角级数简化为 Hurwitz 的 zeta 函数导数的表达式。

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On closed forms of some trigonometric series

We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying the Choi-Srivastava theorem, we reduce these trigonometric series to expressions over Hurwitz's zeta function derivative.

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arXiv - MATH - Classical Analysis and ODEs

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