In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential function.
A more general framework where the term 'exponential polynomial' may be found is that of exponential functions on abelian groups.
They also act as a link between model theory and analytic geometry.
If one defines an exponential variety to be the set of points in Rn where some finite collection of exponential polynomials vanish, then results like Khovanskiǐ's theorem in differential geometry and Wilkie's theorem in model theory show that these varieties are well-behaved in the sense that the collection of such varieties is stable under the various set-theoretic operations as long as one allows the inclusion of the image under projections of higher-dimensional exponential varieties.
Indeed, the two aforementioned theorems imply that the set of all exponential varieties forms an o-minimal structure over R. Exponential polynomials also appear in the characteristic equation associated with linear delay differential equations.