Search results
Results From The WOW.Com Content Network
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. [2] [3] The integers k of this form are sometimes referred to as totatives of n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8.
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
For example, 6 and 35 factor as 6 = 2 × 3 and 35 = 5 × 7, so they are not prime, but their prime factors are different, so 6 and 35 are coprime, with no common factors other than 1. A 24×60 rectangle is covered with ten 12×12 square tiles, where 12 is the GCD of 24 and 60.
There is a larger class of number-theoretic functions that do not fit this definition, for example, the prime-counting functions. This article provides links to functions of both classes. 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.
But the definition was soon extended to functions of several variables and to functions of a complex variable. In the second half of the 19th century, the mathematically rigorous definition of a function was introduced, and functions with arbitrary domains and codomains were defined. Functions are now used throughout all areas of mathematics.
Special functions: non-elementary functions that have established names and notations due to their importance. Trigonometric functions: relate the angles of a triangle to the lengths of its sides. Nowhere differentiable function called also Weierstrass function: continuous everywhere but not differentiable even at a single point.
This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions