A nonconstant function is called periodic if there exists a number that you can add to (or subtract from) the argument and get the same result. The smallest such positive number is called the period. That is, nonconstant function f(x) is periodic, if and only if f(x) = f(x + h) for some real h. The smallest positive such h is the period. For example, the sine function has period 2*pi, and the function g(x) := [x] - x has period 1.
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You can invent any function, to make it periodic. Commonly used functions that are periodic include all the trigonometric functions such as sin and cos (period 2 x pi), tan (period pi). Also, when you work with complex numbers, the exponential function (period 2 x pi x i).
yes
Colour is a property that is not a periodic function.
A power series is a series of the form ( \sum_{n=0}^{\infty} a_n (x - c)^n ), representing a function as a sum of powers of ( (x - c) ) around a point ( c ). In contrast, a Fourier power series represents a periodic function as a sum of sine and cosine functions, typically in the form ( \sum_{n=-\infty}^{\infty} c_n e^{i n \omega_0 t} ), where ( c_n ) are Fourier coefficients and ( \omega_0 ) is the fundamental frequency. While power series are generally used for functions defined on intervals, Fourier series specifically handle periodic functions over a defined period.
no.