Differentially transcendental functions. (English) Zbl 1184.12002

Summary: The aim of this article is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of certain known transcendental differential functions, as of \(\Gamma(x)\). Furthermore, it also determines differential transcendence of solution of some functional equations.


12H05 Differential algebra
12L12 Model theory of fields
03C60 Model-theoretic algebra
12H20 Abstract differential equations
33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
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