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 phi(n), defined as the number of positive integers <=n that are relatively prime to n, where 1 is counted as being relatively prime to all numbers;

2. the function


where (q)_n and (q;q)_n are q-Pochhammer symbols;

3. the Euler L-function L(s), which is a special case of the Artin L-function for the polynomial x^2+1 and is defined by

 L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)),


chi^-(p)={1 for p=1 (mod 4); -1 for p=3 (mod 4)

with (-1/p) a Legendre symbol.

See also

Euler L-function, q-Pochhammer Symbol, Totient Function

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Cite this as:

Weisstein, Eric W. "Euler Function." From MathWorld--A Wolfram Web Resource.

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