Definition
The Taylor series of a real or complex-valued function ƒ(x) that is infinitely differentiable in a neighborhood of a real or complex number a is the power series
which can be written in the more compact sigma notation as
where n! denotes the factorial of n and ƒ (n)(a) denotes the nth derivative of ƒ evaluated at the point a. The derivative of order zero ƒ is defined to be ƒ itself and (x − a)0 and 0! are both defined to be 1. In the case that a = 0, the series is also called a Maclaurin series.
Read more about this topic: Taylor Series
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)