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.