Arithmetic functions

Average order of an arithmetic function

In number theory, an average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average". Let be an arithmetic function. We say that an average order of is if as tends to infinity. It is conventional to choose an approximating function that is continuous and monotone. But even so an average order is of course not unique. In cases where the limit exists, it is said that has a mean value (average value) . (Wikipedia).

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Average or Central Tendency: Arithmetic Mean, Median, and Mode

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From playlist ck12.org Algebra 1 Examples

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From playlist Calculus

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From playlist Applications of Definite Integration

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From playlist Algebra

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From playlist Determining Inverse Functions

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From playlist Order of Operations

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From playlist Introduction to Functions: Function Basics

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From playlist Mathematics

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From playlist The Sato-Tate conjecture for abelian varieties

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From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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From playlist CTNT 2018 - "Arithmetic Statistics" by Álvaro Lozano-Robledo

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From playlist Mathematics

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Average Value

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From playlist Integration Intro

Related pages

Monotonic function | Multiplicative function | Finite field | Divisor summatory function | Euler product | Indicator function | Continuous function | Normal order of an arithmetic function | Divisor sum identities | Euler's totient function | Von Mangoldt function | Cauchy product | Arithmetic function | Monic polynomial | Divisor | Möbius function | Extremal orders of an arithmetic function | Number theory | Natural density | Prime number theorem | Dirichlet series | Riemann zeta function | Divisor function