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The algebraic periods as a subset of the complex numbers. In mathematics, specifically algebraic geometry, a period or algebraic period[1] is a complex number that can be expressed as an integral of an algebraic function over an algebraic domain. The periods are a class of numbers which includes, alongside the algebraic numbers, many well known ...
Periodic function. A periodic function also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle. [1] For example, the trigonometric functions, which repeat at intervals of radians, are periodic functions.
A (purely) periodic sequence (with period p), or a p-periodic sequence, is a sequence a 1, a 2, a 3, ... satisfying . a n+p = a n. for all values of n. [1] [2] [3] If a sequence is regarded as a function whose domain is the set of natural numbers, then a periodic sequence is simply a special type of periodic function.
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element.
v. t. e. Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry ...
The period of 1 / p 2 is usually pT p, where T p is the period of 1 / p . There are three known primes for which this is not true, and for those the period of 1 / p 2 is the same as the period of 1 / p because p 2 divides 10 p−1 −1. These three primes are 3, 487, and 56598313 (sequence A045616 in the OEIS). [12]
List of periodic functions. This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
A period-one point is called a fixed point. The logistic map. exhibits periodicity for various values of the parameter r. For r between 0 and 1, 0 is the sole periodic point, with period 1 (giving the sequence 0, 0, 0, …, which attracts all orbits). For r between 1 and 3, the value 0 is still periodic but is not attracting, while the value is ...