For any (where denotes the set of algebraic numbers), let denote the maximum of moduli of all conjugates of . Then a function
is said to be an E-function if the following conditions hold (Nesterenko 1999).
2. If is any positive number, then as .
3. For any , there exists a sequence of natural numbers such that for , ..., and that .
Every E-function is an entire function, and the set of E-functions is a ring under the operations of addition and multiplication. Furthermore, if is an E-function, then and are E-functions, and for any algebraic number , the function is also an E-function (Nesterenko 1999).