D-Algebraic Functions and their Discrete Analog

An algebraic differential equation is an equation that can be written in the form P=0, where P is a multivariate polynomial in the independent variable and derivatives of the dependent variable. Solutions to such equations are called differentially algebraic functions. These functions naturally appear in enumerative combinatorics, context-free grammars, and automata theory.

I will introduce classes of D-algebraic functions and their discrete analog. We will discuss their closure properties and conclude with a recent result from joint work with James Worrell related to a subclass of discrete dynamical systems.