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Tanaka, Hidekazu

Transcendence of special values of log double sine function. (English) Zbl 1310.11076

Proc. Japan Acad., Ser. A 90, No. 9, 133-134 (2014).
Summary: In [J. Number Theory 129, No. 9, 2154–2165 (2009; Zbl 1175.11039); ibid. 130, No. 5, 1251 (2010; Zbl 1216.11070)], S. Gun et al. 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.

MSC:

11J81 Transcendence (general theory)
11J86 Linear forms in logarithms; Baker’s method
11J91 Transcendence theory of other special functions

Keywords:

double sine function; transcendency; Catalan constant

Citations:

Zbl 1175.11039; Zbl 1216.11070
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\textit{H. Tanaka}, Proc. Japan Acad., Ser. A 90, No. 9, 133--134 (2014; Zbl 1310.11076)
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References:

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