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A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive [2] constant P with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period.
Since the period has length , which is an even number, the convergent producing the fundamental solution is obtained by truncating the continued fraction right before the end of the first occurrence of the period: [;,,] =. The sequence of convergents for the square root of seven are
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, 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 mathematical constants such as the number π .
Given a mapping f from a set X into itself, :, a point x in X is called periodic point if there exists an n >0 so that = where f n is the n th iterate of f.The smallest positive integer n satisfying the above is called the prime period or least period of the point x.
We may graphically solve for as the intersection of two curves in the (,) plane: {= + = For fixed ,,, the second curve is a fixed hyperbola in the first quadrant. The first curve is a parabola with shape y = 9 16 β 2 ( z 2 ) 2 {\textstyle y={\tfrac {9}{16}}\beta ^{2}(z^{2})^{2}} , and apex at location ( 4 3 β ( ω 2 − α ) , δ 2 ω 2 ...
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The period of c / k , for c coprime to k, equals the period of 1 / k . If k = 2 a ·5 b n where n > 1 and n is not divisible by 2 or 5, then the length of the transient of 1 / k is max( a , b ), and the period equals r , where r is the multiplicative order of 10 mod n, that is the smallest integer such that 10 r ≡ 1 (mod ...
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related to: how to solve for period- 1717 Olentangy River Rd, Columbus, OH · Directions · (614) 298-1070
