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:
“If photography is allowed to stand in for art in some of its functions it will soon supplant or corrupt it completely thanks to the natural support it will find in the stupidity of the multitude. It must return to its real task, which is to be the servant of the sciences and the arts, but the very humble servant, like printing and shorthand which have neither created nor supplanted literature.”
—Charles Baudelaire (1821–1867)