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:
“In former times and in less complex societies, children could find their way into the adult world by watching workers and perhaps giving them a hand; by lingering at the general store long enough to chat with, and overhear conversations of, adults...; by sharing and participating in the tasks of family and community that were necessary to survival. They were in, and of, the adult world while yet sensing themselves apart as children.”
—Dorothy H. Cohen (20th century)
“I often used to think myself in the case of the fox-hunter, who, when he had toiled and sweated all day in the chase as if some unheard-of blessing was to crown his success, finds at last all he has got by his labor is a stinking nauseous animal. But my condition was yet worse than his; for he leaves the loathsome wretch to be torn by his hounds, whilst I was obliged to fondle mine, and meanly pretend him to be the object of my love.”
—Sarah Fielding (1710–1768)