@Article{Ogawara2017,
author = "Ogawara, Hiroshi",
title = "On criteria for algebraic independence of collections of functions satisfying algebraic difference relations",
journal = "Opuscula Math.",
year = "2017",
volume = "37",
number = "3",
pages = "457--472",
doi = "http://dx.doi.org/10.7494/OpMath.2017.37.3.457",
url = "http://dx.doi.org/10.7494/OpMath.2017.37.3.457",
abstract = "This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1) Vignéras' multiple gamma functions and derivatives of the gamma function, (2) the logarithmic function, \(q\)-exponential functions and \(q\)-polylogarithm functions. In a similar way, we give a generalization of Ostrowski's theorem.",
keywords = "difference algebra, systems of algebraic difference equations, algebraic independence, Vignéras' multiple gamma functions, \(q\)-polylogarithm functions",
issn = "1232-9274"
}