Harmonic numbers as the summation of integrals

2021/12/01 by N. Karjanto, Karjanto, N.
Computer Science · Mathematics · #01A05 #97I30 #97I50 #FOS: Computer and information sciences #FOS: Mathematics #General Literature (cs.GL) #History and Overview (math.HO) #cs.GL #math.HO #msc:01A05 #msc:97I30 #msc:97I50

paper · pdf · doi:10.48550/arxiv.2112.00257

4 pages, 16 references

arxiv created 2021/12/01 · arxiv updated 2021/12/02

Abstract

Harmonic numbers arise from the truncation of the harmonic series. The n^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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