New harmonic number series
Kunle Adegoke, Robert Frontczak
TL;DR
This paper introduces new closed-form series involving harmonic numbers and inverse factorials, simplifying the derivation of known quadratic Euler sums and expanding the mathematical understanding of harmonic series.
Contribution
It presents novel closed-form expressions for harmonic number series and offers a simpler derivation of a well-known quadratic Euler sum.
Findings
New closed forms for harmonic series involving inverse factorials
Simplified derivation of a famous quadratic Euler sum
Enhanced understanding of harmonic number series representations
Abstract
Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived. A high point of the presentation is the rediscovery, by much simpler means, of a famous quadratic Euler sum originally discovered in 1995 by Borwein and Borwein.
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Taxonomy
TopicsMathematical functions and polynomials · Differential Equations and Boundary Problems · Analytic and geometric function theory