Euler sums and integral connections
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Sofo, Anthony 
ORCID: 0000-0002-1277-8296 and Nimbran, Amrik Singh ORCID: 0000-0001-8934-0826
(2019)
Euler sums and integral connections.
Mathematics, 7 (9).
ISSN 2227-7390
Abstract
In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler's work on the subject followed by notations used in the body of the paper. After discussing some alternating Euler sums, we investigate the connection of integrals of inverse trigonometric and hyperbolic type functions to generate many new Euler sum identities. We also give some new identities for Catalan's constant, Apery's constant and a fast converging identity for the famous ζ(2) constant.
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| Item type | Article |
| URI | https://vuir.vu.edu.au/id/eprint/45963 |
| DOI | 10.3390/math7090833 |
| Official URL | https://www.mdpi.com/2227-7390/7/9/833 |
| Subjects | Current > FOR (2020) Classification > 4901 Applied mathematics Current > Division/Research > College of Science and Engineering |
| Keywords | applied mathematics, maths, Euler sums, harmonic numbers, odd harmonic numbers |
| Citations in Scopus | 11 - View on Scopus |
| Download/View statistics | View download statistics for this item |
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