General Case
For the special case of, there is a closely related set of polynomials, also called the Newton polynomials, that are simply the binomial coefficients for general argument. That is, one also has the Newton polynomials given by
In this form, the Newton polynomials generate the Newton series. These are in turn a special case of the general difference polynomials which allow the representation of analytic functions through generalized difference equations.
Read more about this topic: Newton Polynomial
Famous quotes containing the words general and/or case:
“As a general rule, do not kick the shins of the opposite gentleman under the table, if personally unaquainted with him; your pleasantry is liable to be misunderstood—a circumstance at all times unpleasant.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“The attention of those who frequent the camp-meetings at Eastham is said to be divided between the preaching of the Methodists and the preaching of the billows on the back side of the Cape, for they all stream over here in the course of their stay. I trust that in this case the loudest voice carries it. With what effect may we suppose the ocean to say, “My hearers!” to the multitude on the bank. On that side some John N. Maffit; on this, the Reverend Poluphloisboios Thalassa.”
—Henry David Thoreau (1817–1862)