Generating Functions
The Dirichlet series for φ(n) may be written in terms of the Riemann zeta function as:
The Lambert series generating function is
which converges for |q| < 1.
Both of these are proved by elementary series manipulations and the formulae for φ(n).
Read more about this topic: Euler's Totient Function
Famous quotes containing the word functions:
“Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.”
—Kate Millett (b. 1934)