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 qPochhammer symbols;
3. the Euler Lfunction , which is a special case of the Artin Lfunction for the polynomial and is defined by
(4)

where
(5)
 
(6)

with a Legendre symbol.