Euler Function

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.