## 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.

### 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
Full Text:

### References:

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