The Function Is Smooth
The function f has continuous derivatives of all orders in all points x of the real line, given by
where pn(x) is a polynomial of degree n − 1 given recursively by p1(x) = 1 and
Read more about this topic: Non-analytic Smooth Function
Famous quotes containing the words function and/or smooth:
“Literature does not exist in a vacuum. Writers as such have a definite social function exactly proportional to their ability as writers. This is their main use.”
—Ezra Pound (1885–1972)
“It may seem strange that any road through such a wilderness should be passable, even in winter, when the snow is three or four feet deep, but at that season, wherever lumbering operations are actively carried on, teams are continually passing on the single track, and it becomes as smooth almost as a railway.”
—Henry David Thoreau (1817–1862)