In mathematics, any integrable function can be made into a periodic function with period P by summing the translations of the function by integer multiples of P. This is called periodic summation:
Quotient space as domain
If a periodic function is instead represented using the quotient spacedomain \mathbb{R}/(P\mathbb{Z}) then one can write: :\varphi_P : \mathbb{R}/(P\mathbb{Z}) \to \mathbb{R} :\varphi_P(x) = \sum_{\tau\in x} s(\tau) ~ . The arguments of \varphi_P are equivalence classes of real numbers that share the same fractional part when divided by P. == Citations ==