# Taylor Series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

The concept of a Taylor series was formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor series is centered at zero, then that series is also called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century.

It is common practice to approximate a function by using a finite number of terms of its Taylor series. Taylor's theorem gives quantitative estimates on the error in this approximation. Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial. The Taylor series of a function is the limit of that function's Taylor polynomials, provided that the limit exists. A function may not be equal to its Taylor series, even if its Taylor series converges at every point. A function that is equal to its Taylor series in an open interval (or a disc in the complex plane) is known as an analytic function.

### Other articles related to "taylor series, series, taylor":

Logrithm - Calculation - Power Series
... Taylor series For any real number z that satisfies 0 < z < 2, the following formula holds This is a shorthand for saying that ln(z) can be approximated to a more and more accurate ... This series approximates ln(z) with arbitrary precision, provided the number of summands is large enough ... elementary calculus, ln(z) is therefore the limit of this series ...
Divided Differences - Alternative Definitions - Taylor Form - Higher Order
... The Taylor series or any other representation with function series can in principle be used to approximate divided differences ... Taylor series are infinite sums of power functions ... Regular Taylor series is a weighted sum of power functions Taylor series for divided differences We know that the first terms vanish, because we have a ...
David W. Taylor - Early Life and Career
... Taylor was born in Louisa County, Va ... In August 1886, Taylor was appointed an assistant naval constructor ... In probably the greatest achievement of his career he created the "Taylor Standard Series" of 80 models with systematically varying proportions and prismatic coefficient ...
Fractional Taylor Series
... With the emergence of fractional calculus, a natural question arises about what the Taylor Series expansion would be ... limit as we approach from the right, the fractional Taylor series can be written as ...
Binary Entropy Function - Taylor Series
... The Taylor series of the binary entropy function in a neighborhood of 1/2 is for. ...

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