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Τι (ποιος) είναι function-theoretic - ορισμός

ANY FUNCTION WHOSE DOMAIN IS THE POSITIVE INTEGERS AND WHOSE RANGE IS A SUBSET OF THE COMPLEX NUMBERS

Arithmetic functions; Arithmetical function; Number-theoretic function; Number-theoretic functions; Number theoretic function; Arithmetical functions; Summatory function

Arithmetic function

In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authorsNiven & Zuckerman, 4.2.

https://en.wikipedia.org/wiki/Arithmetic_function

Functional-theoretic algebra

Functional Theoretic Algebra; Functional theoretic algebra; Functional-Theoretic Algebra

Any vector space can be made into a unital associative algebra, called functional-theoretic algebra, by defining products in terms of two linear functionals. In general, it is a non-commutative algebra.

https://en.wikipedia.org/wiki/Functional-theoretic_algebra

Function (mathematics)

$A binary operation is a typical example of a bivariate function which assigns to each pair <math>(x, y)</math> the result <math>x\circ y</math>.$

ASSOCIATION OF A SINGLE OUTPUT TO EACH INPUT

Mathematical Function; Mathematical function; Function specification (mathematics); Mathematical functions; Empty function; Function (math); Ambiguous function; Function (set theory); Function (Mathematics); Functions (mathematics); Domain and range; Functional relationship; G(x); H(x); Function notation; Output (mathematics); Ƒ(x); Overriding (mathematics); Overriding union; F of x; Function of x; Bivariate function; Functional notation; Function of several variables; Y=f(x); ⁡; Draft:The Repeating Fractional Function; Image (set theory); Mutivariate function; Draft:Specifying a function; Function (maths); Functions (math); Functions (maths); F(x); Empty map; Function evaluation

In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously.

https://en.wikipedia.org/wiki/Function_(mathematics)

Βικιπαίδεια

Arithmetic function

In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n".

An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n.

There is a larger class of number-theoretic functions that do not fit the above definition, for example, the prime-counting functions. This article provides links to functions of both classes.

Arithmetic functions are often extremely irregular (see table), but some of them have series expansions in terms of Ramanujan's sum.

https://en.wikipedia.org/wiki/Arithmetic function