The term "Euler function" may be used to refer to any of several functions in number theory and the theory of special functions, including
1. the totient function 
, defined as the number of positive
integers 
that are relatively prime to 
, where 1 is counted as being relatively
prime to all numbers;
2. the function
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
and 
are q-Pochhammer symbols;
3. the Euler L-function 
, which is a special case of the Artin
L-function for the polynomial 
and is defined by
 |
(4)
|
where
 |  |  |
(5)
|
 |  |  |
(6)
|
with 
a Legendre symbol.
