Constant Function

A Function $f(x)=c$ which does not change as its parameters vary. The Graph of a 1-D constant Function is a straight Line. The Derivative of a constant Function $c$ is

$${d\over dx} c=0,$$ (1)

and the Integral is

$$\int c\,dx = cx.$$ (2)

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

$${\mathcal F}[1] =\int_{-\infty}^\infty e^{-2\pi ikx}\,dx = \delta(k),$$ (3)

where $\delta(k)$ is the Delta Function.

See also Fourier Transform--1

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.