Definition of Summatory. Meaning of Summatory. Synonyms of Summatory

- In number theory, the totient summatory function Φ ( n ) {\displaystyle \Phi (n)} is a summatory function of Euler's totient function defined by: Φ ( n...
- In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic...
- {\displaystyle \alpha ^{-1}} -weighted summatory functions are related to the Mertens function, or weighted summatory functions of the Moebius function. In...
- number of prime factors. Equivalently, it can be stated in terms of the summatory Liouville function, with the conjecture being that L ( n ) = ∑ k = 1 n...
- 10001 Weisstein, Eric W. "Chebyshev functions". MathWorld. "Mangoldt summatory function". PlanetMath. "Chebyshev functions". PlanetMath. Riemann's Explicit...
- {\displaystyle \Omega (n)\sim {\frac {\log n}{\log 2}}} . Asymptotics for the summatory functions over ω ( n ) {\displaystyle \omega (n)} , Ω ( n ) {\displaystyle...
- Moebius function. Another unique Dirichlet series identity generates the summatory function of some arithmetic f evaluated at GCD inputs given by ∑ n ≥ 1...
- real constant. Given an additive function f {\displaystyle f} , let its summatory function be defined by M f ( x ) := ∑ n ≤ x f ( n ) {\textstyle {\mathcal...
- the Dirichlet divisor problem of computing asymptotic estimates for the summatory function of the divisor function. From we have ∑ d = 1 n M ( ⌊ n / d ⌋...
- obtained the currently best O-estimates for the remainder terms of the summatory functions of both the sum-of-divisors function σ {\displaystyle \sigma...