Bell Series of an Arithmetical Function : Number Theory #Bell #Series #of #an #Arithmetical #Function #: #Number #Theory
E. T. Bell used formal power series to study properties of multiplicative arithmetical functions . Definition : [ Bell Series ] Given an arithmetical function f and a prime p , we denote by f p (x) the formal power series f p (x) = 𝜮 f(p n ) x n and call this the Bell series of f modulo p. Note : Bell series are especially useful when f is multiplicative. Examples : · The Bell series for the Mobius function 𝛍 is given by 𝛍 p (x) = 1-x. · The Bell series for the Euler ‘s totient function ⲫ is given by ⲫ p (x) = (1-x) / (1-px) · The Bell series ...