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Article

Euler Sums and Integral Connections

1
College of Engineering and Science, Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia
2
B3-304, Palm Grove Heights, Ardee City, Gurugram, Haryana 122003, India
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 833; https://doi.org/10.3390/math7090833
Received: 13 August 2019 / Revised: 3 September 2019 / Accepted: 4 September 2019 / Published: 9 September 2019
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
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. View Full-Text
Keywords: Euler sums; Catalan’s constant; Trigamma function; integral representation; closed form; ArcTan and ArcTanh functions; partial fractions Euler sums; Catalan’s constant; Trigamma function; integral representation; closed form; ArcTan and ArcTanh functions; partial fractions
MDPI and ACS Style

Sofo, A.; Nimbran, A.S. Euler Sums and Integral Connections. Mathematics 2019, 7, 833. https://doi.org/10.3390/math7090833

AMA Style

Sofo A, Nimbran AS. Euler Sums and Integral Connections. Mathematics. 2019; 7(9):833. https://doi.org/10.3390/math7090833

Chicago/Turabian Style

Sofo, Anthony, and Amrik S. Nimbran 2019. "Euler Sums and Integral Connections" Mathematics 7, no. 9: 833. https://doi.org/10.3390/math7090833

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