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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.
Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers , that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals.
All trigonometric functions are periodic functions of period 2 π. This is the smallest period, except for the tangent and the cotangent, which have π as smallest period. This means that, for every integer k , one has
The doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension. Familiar examples of functions with a single period on the real number line include the trigonometric functions like cosine and sine , In the complex plane the exponential function e z is a singly ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
If every point in X is a periodic point with the same period n, then f is called periodic with period n (this is not to be confused with the notion of a periodic function). If there exist distinct n and m such that = then x is called a preperiodic point. All periodic points are preperiodic.
More than 38 million Americans have diabetes, and between 90% and 95% of them have type 2 diabetes. While most are adults over the age of 45, an increasing number of children and teens are also ...
The graph of the Dirac comb function is an infinite series of Dirac delta functions spaced at intervals of T. In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula := = for some given period . [1]