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:
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)