In mathematics, E-functions are a type of power series that satisfy particular arithmetic conditions on the coefficients.
They are of interest in transcendental number theory, and are closely related to G-functions.
A power series with coefficients in the field of algebraic numbers is called an E-function[1] if it satisfies the following three conditions: The second condition implies that f is an entire function of x. E-functions were first studied by Siegel in 1929.
[2] He found a method to show that the values taken by certain E-functions were algebraically independent.
[3] Since then these functions have proved somewhat useful in number theory and in particular they have application in transcendence proofs and differential equations.