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).
