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November 2014 Transcendence of special values of log double sine function
Hidekazu Tanaka
Proc. Japan Acad. Ser. A Math. Sci. 90(9): 133-134 (November 2014). DOI: 10.3792/pjaa.90.133

Abstract

In 2009~[4,5], S. Gun, M. R. Murty, P. Rath studied transcendental values of the logarithm of the gamma function. They showed that for any rational number $x$ with $0 < x < \frac{1}{2}$, the number $\log \Gamma(x) + \log \Gamma(1-x)$ is transcendental with at most one possible exception. In this paper, we study transcendental values of log double sine function using their method.

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Hidekazu Tanaka. "Transcendence of special values of log double sine function." Proc. Japan Acad. Ser. A Math. Sci. 90 (9) 133 - 134, November 2014. https://doi.org/10.3792/pjaa.90.133

Information

Published: November 2014
First available in Project Euclid: 6 November 2014

zbMATH: 1310.11076
MathSciNet: MR3277205
Digital Object Identifier: 10.3792/pjaa.90.133

Subjects:
Primary: 11M36

Keywords: Catalan constant , double sine function , transcendency

Rights: Copyright © 2014 The Japan Academy

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Vol.90 • No. 9 • November 2014
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