https://reference.wolfram.com › language › ref › Series.html

Series[f, x -> x0] generates the leading term of a power series expansion for f about the point x = x0. Series[f, {x, x0, nx}, {y, y0, ny}, ...] successively finds series expansions with respect to x, then y, etc.

https://reference.wolfram.com › language › guide › SeriesExpansions.html

Series Expansions. Power series are in many ways the algebraic analog of limited-precision numbers. The Wolfram Language can generate series approximations to virtually any combination of built-in mathematical functions. It will then automatically combine series, truncating to the correct order.

https://mathematica.stackexchange.com › questions › 264230 › how-to-get-the-n-order-taylor...

I want to get the n-order Taylor expansion of a bivariate function at point (x0,y0): f[x_, y_]: = E^(x + y); {x0,y0}={0,0}; The result calculated by hand is: $\begin{aligned} \mathrm{e}^{x+y}...

https://www.wolframalpha.com › widgets › view.jsp

A calculator for finding the expansion and form of the Taylor Series of a given function. To find the Maclaurin Series simply set your Point to zero (0).

https://mathworld.wolfram.com › TaylorSeries.html

A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) If a=0, the expansion is known as a Maclaurin series. Taylor's theorem (actually discovered first by Gregory) states that any function satisfying certain conditions can be expressed as a Taylor series. The Taylor (or more general ...

https://www.wolframalpha.com › input ›

Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals.

https://mathematica.stackexchange.com › ... › how-to-prepare-expression-for-taylor-expansion

with the assumption that M ≫ m M ≫ m and the need to expand it up to order O(M−2) O (M − 2). By hand, I would first rearrange the terms in the expression such that they only depend on m/M m / M and then Taylor this new expression, substituting m/M ≡ z m / M ≡ z, using Series[...,{z,0,2}].

https://www.wolframalpha.com › examples › mathematics › calculus-and-analysis › series-expansions

Find a Laurent series expansion: series cot z. series (sin z)/z^3 to order 10. series exp (1/x) at x = infinity. Get answers to your series expansion questions with interactive calculators. Solve Taylor, Laurent or Puiseux series expansion problems.

https://reference.wolfram.com › language › tutorial › SeriesLimitsAndResidues.html

When you make a power series expansion in a variable x, the Wolfram Language assumes that all objects that do not explicitly contain x are in fact independent of x. Series thus does partial derivatives (effectively using D ) to build up Taylor series.