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# What is the difference between a Taylor and Maclaurin series?

## What is the difference between a Taylor and Maclaurin series?

The Taylor Series, or Taylor Polynomial, is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. A Maclaurin Polynomial, is a special case of the Taylor Polynomial, that uses zero as our single point.

What is the difference between Taylor series and Taylor polynomial?

The difference between a Taylor polynomial and a Taylor series is the former is a polynomial, containing only a finite number of terms, whereas the latter is a series, a summation of an infinite set of terms, any number of which (including an infinite number) may be zero.

What is the Taylor and Maclaurin series used for?

Taylor Series and Maclaurin Series are very important when we want to express a function as a power series. For example, e x e^{x} ex and cos ⁡ x \cos x cosx can be expressed as a power series!

### What is the difference between power series and Taylor series?

As the names suggest, the power series is a special type of series and it is extensively used in Numerical Analysis and related mathematical modelling. Taylor series is a special power series that provides an alternative and easy-to-manipulate way of representing well-known functions.

Is Maclaurin and Taylor same?

A Maclaurin series is the expansion of the Taylor series of a function about zero. The Taylor series got its name from Brook Taylor. Brook Taylor was an English mathematician in 1715. The Maclaurin series is named after Colin Maclaurin.

What makes a Maclaurin series?

Maclaurin series are a type of series expansion in which all terms are nonnegative integer powers of the variable.

## What is the use of Taylor series?

The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point.

What is the Taylor series of a polynomial?

For polynomials, the Taylor series around x=0 is just the polynomial itself. If you want the series around x=a, the general formula (for a function f around x=a) f(a)+f′(a)(x−a)+f″(a)2!( x−a)2+⋯+f(n)(a)n!( x−a)n.

Where is Taylor series used?

That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point.

### Who discovered Maclaurin series?

Colin Maclaurin

Colin Maclaurin
Known for Euler–Maclaurin formula Maclaurin’s inequality Maclaurin series Maclaurin spheroid Maclaurin–Cauchy test Braikenridge–Maclaurin theorem Trisectrix of Maclaurin
Awards Grand Prize of the French Academy of Sciences
Scientific career
Fields Mathematician, child prodigy

Is Maclaurin series A power series?

A Maclaurin series is a power series that allows one to calculate an approximation of a function f ( x ) f(x) f(x) for input values close to zero, given that one knows the values of the successive derivatives of the function at zero. In many practical applications, it is equivalent to the function it represents.

Does every function have a Taylor series?

Not every function is analytic. The video below explores the different ways in which a Taylor series can fail to converge to a function f(x). The function may not be infinitely differentiable, so the Taylor series may not even be defined.