调和数作为积分的总和

arXiv - CS - General Literature Pub Date : 2021-12-01 DOI:arxiv-2112.00257

N. Karjanto

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引用次数: 0

摘要

谐波数产生于谐波级数的截断。$n^\text{th}$调和数是$n$以下的每个正整数的倒数之和。除了简要介绍调和数的性质外，我们还将调和数作为涉及指数函数和双曲正割函数乘积的积分和。这个证明是比较简单的，因为它只包含数学归纳法原理和分部积分法。

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Harmonic numbers as the summation of integrals

Harmonic numbers arise from the truncation of the harmonic series. The $n^\text{th}$ harmonic number is the sum of the reciprocals of each positive integer up to $n$. In addition to briefly introducing the properties of harmonic numbers, we cover harmonic numbers as the summation of integrals that involve the product of exponential and hyperbolic secant functions. The proof is relatively simple since it only comprises the Principle of Mathematical Induction and integration by parts.

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arXiv - CS - General Literature

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