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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.

MSC:
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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Full Text: Euclid