Bell series

In mathematics, the Bell series is a formal power series used to study properties of arithmetical functions. Bell series were introduced and developed by Eric Temple Bell.

Given an arithmetic function ${\displaystyle f}$ and a prime ${\displaystyle p}$, define the formal power series ${\displaystyle f_{p}(x)}$, called the Bell series of ${\displaystyle f}$ modulo ${\displaystyle p}$ as:

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