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Constant Function


ConstantFunction
ConstantFunctionReIm

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line.

The derivative of a constant function c is

 d/(dx)c=0,
(1)

and the integral is

 intcdx=cx.
(2)

The Fourier transform of the constant function f(x)=1 is given by

 F_x[1](k)=int_(-infty)^inftye^(-2piikx)dx=delta(k),
(3)

where delta(k) is the delta function.


See also

Constant Map, Identity Function, Linear Function, Piecewise Constant Function, Fourier Transform--1, Zero Function

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References

Spanier, J. and Oldham, K. B. "The Constant Function c." Ch. 1 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 11-14, 1987.

Referenced on Wolfram|Alpha

Constant Function

Cite this as:

Weisstein, Eric W. "Constant Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConstantFunction.html

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