A Quadratic Harmonic Approximation
Mark B. Villarino
TL;DR
This paper presents a straightforward method to derive the quadratic term in Euler's asymptotic expansion of the nth harmonic number, enhancing understanding of its precise asymptotic behavior.
Contribution
It introduces a simple modification of Young's elementary approach to accurately compute the quadratic term in the harmonic number's asymptotic expansion.
Findings
Derived the quadratic term in Euler's asymptotic expansion.
Provided a simplified method for harmonic number approximation.
Enhanced the accuracy of harmonic number asymptotics.
Abstract
We obtain the quadratic term in Euler's asymptotic expansion of the nth harmonic number by a simple modification of Young's elementary determination of the linear term.
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Taxonomy
TopicsMathematics and Applications · Advanced Mathematical Theories and Applications · History and Theory of Mathematics