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t. e. In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where representations that differ only in the order of the summands or in the signs of the numbers being squared are counted as different.
The divisor summatory function is defined as. where. is the divisor function. The divisor function counts the number of ways that the integer n can be written as a product of two integers. More generally, one defines. where dk (n) counts the number of ways that n can be written as a product of k numbers. This quantity can be visualized as the ...
Sum of cubes of divisors, σ 3 (n) up to n = 250. In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer (including 1 and the number itself). It appears in a number of ...
Divisor sum identities. The purpose of this page is to catalog new, interesting, and useful identities related to number-theoretic divisor sums, i.e., sums of an arithmetic function over the divisors of a natural number , or equivalently the Dirichlet convolution of an arithmetic function with one: These identities include applications to sums ...
The geometric series is an infinite series derived from a special type of sequence called a geometric progression, which is defined by just two parameters: the initial term and the common ratio . Finite geometric series have a third parameter, the final term's power.
Aggregate function. In database management, an aggregate function or aggregation function is a function where multiple values are processed together to form a single summary statistic. (Figure 1) Entity relationship diagram representation of aggregation. Common aggregate functions include: Others include: Formally, an aggregate function takes ...
Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.