Differentially Transcendental Functions

Zarko Mijajlovic; Branko Malesevic

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Differentially Transcendental Functions

Zarko Mijajlovic·Branko Malesevic

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Abstract

The aim of this paper 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 $Γ(x)$. Furthermore, it also determines differential transcendency of solution of some functional equations.

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Zarko Mijajlovic, Branko Malesevic. 2008-04-15. Differentially Transcendental Functions. https://arxiv.org/abs/math/0412354

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