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

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.


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


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