Arithmetic Functions' Bell Series
Definition 1
Given the arithmetic function $f$ and prime number $p$, the following $f_{p}(x)$ is defined as the Bell series of $f$ modulo $p$. $$ f_{p}(x) := \sum_{n=0}^{\infty} f \left( p^{n} \right) x^{n} $$
Apostol. (1976). Introduction to Analytic Number Theory: p42. ↩︎