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) |