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June 2019 Erdősian functions and an identity of Gauss
Tapas Chatterjee, Suraj Singh Khurana
Proc. Japan Acad. Ser. A Math. Sci. 95(6): 58-63 (June 2019). DOI: 10.3792/pjaa.95.58

Abstract

A famous identity of Gauss gives a closed form expression for the values of the digamma function $\psi(x)$ at rational arguments $x$ in terms of elementary functions. Linear combinations of such values are intimately connected with a conjecture of Erdős which asserts non vanishing of an infinite series associated to a certain class of periodic arithmetic functions. In this note we give a different proof for the identity of Gauss using an orthogonality like relation satisfied by these functions. As a by product we are able to give a new interpretation for $n$th Catalan number in terms of these functions.

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Tapas Chatterjee. Suraj Singh Khurana. "Erdősian functions and an identity of Gauss." Proc. Japan Acad. Ser. A Math. Sci. 95 (6) 58 - 63, June 2019. https://doi.org/10.3792/pjaa.95.58

Information

Published: June 2019
First available in Project Euclid: 31 May 2019

zbMATH: 07137913
MathSciNet: MR3960282
Digital Object Identifier: 10.3792/pjaa.95.58

Subjects:
Primary: 05A19, 11M35, 33E99

Rights: Copyright © 2019 The Japan Academy

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Vol.95 • No. 6 • June 2019
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