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t. e. In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.
Passions. Passions is an American television soap opera that originally aired on NBC from July 5, 1999, to September 7, 2007, and on DirecTV 's The 101 Network from September 17, 2007, to August 7, 2008. Created by screenwriter James E. Reilly and produced by NBC Studios, Passions follows the lives, loves and various romantic and paranormal ...
Tabitha. (TV series) Tabitha is an American fantasy sitcom and a spin-off of Bewitched that aired on ABC from September 10, 1977, to January 14, 1978. The series starred Lisa Hartman in the title role as Tabitha Stephens, the witch daughter of Samantha and Darrin Stephens who was introduced on Bewitched during its second season. In the series ...
v. t. e. In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function, the Taylor polynomial is the truncation at the order of the Taylor series of the function.
The classic late-'60s sitcom "Bewitched" starred Elizabeth Montgomery as the beautiful and magically gifted Samantha, but a pint-sized co-star often stole the scene: Erin Murphy, who played little ...
In mathematics, the Bernoulli numbers B n are a sequence of rational numbers which occur frequently in analysis.The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain ...
Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. The partial sum formed by the first n + 1 terms of a Taylor ...
Universal Taylor series. A universal Taylor series is a formal power series , such that for every continuous function on , if , then there exists an increasing sequence of positive integers such that. In other words, the set of partial sums of is dense (in sup-norm) in , the set of continuous functions on that is zero at origin.