Euler Sums and Integral Connections

Anthony Sofo and Amrik Singh Nimbran
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Anthony Sofo: College of Engineering and Science, Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia
Amrik Singh Nimbran: B3-304, Palm Grove Heights, Ardee City, Gurugram, Haryana 122003, India

Mathematics, 2019, vol. 7, issue 9, 1-24

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.

Keywords: Euler sums; Catalan’s constant; Trigamma function; integral representation; closed form; ArcTan and ArcTanh functions; partial fractions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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