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).

1. All coefficients
belong to the same number field of finite degree over Q.

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).

Nesterenko, Yu. V. A Course on Algebraic Independence: Lectures at IHP 1999. Unpublished manuscript. 1999.Siegel, C. L.
Transcendental
Numbers. New York: Chelsea, 1965.