Differentially transcendental functions
Copyright policy )Differentially transcendental functions
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 $��(x)$. Furthermore, it also determines differential transcendency of solution of some functional equations.
- University of Belgrade Serbia
differentially transcendental functions, Abstract differential equations, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), not solutions of algebraic differential equations, Model-theoretic algebra, Mathematics - Logic, Differential algebra, analytic functions, differential transcendence of solutions of functional equations, General Mathematics (math.GM), 65L80, 34A09, 12H05, FOS: Mathematics, Logic (math.LO), Mathematics - General Mathematics, Model theory of fields
differentially transcendental functions, Abstract differential equations, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), not solutions of algebraic differential equations, Model-theoretic algebra, Mathematics - Logic, Differential algebra, analytic functions, differential transcendence of solutions of functional equations, General Mathematics (math.GM), 65L80, 34A09, 12H05, FOS: Mathematics, Logic (math.LO), Mathematics - General Mathematics, Model theory of fields
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