Mijajlović, Žarko; Malešević, Branko Differentially transcendental functions. (English) Zbl 1184.12002 Bull. Belg. Math. Soc. - Simon Stevin 15, No. 2, 193-201 (2008). 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. Cited in 5 Documents 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) Keywords:analytic functions; not solutions of algebraic differential equations; differentially transcendental functions; differential transcendence of solutions of functional equations PDF BibTeX XML Cite \textit{Ž. Mijajlović} and \textit{B. Malešević}, Bull. Belg. Math. Soc. - Simon Stevin 15, No. 2, 193--201 (2008; Zbl 1184.12002) Full Text: arXiv Euclid OpenURL