# Series

Series[f,{x,x0,n}]

generates a power series expansion for f about the point x=x0 to order (x-x0)n.

Series[f,{x,x0,nx},{y,y0,ny},]

successively finds series expansions with respect to x, then y, etc.

# Details and Options • Series can construct standard Taylor series, as well as certain expansions involving negative powers, fractional powers, and logarithms.
• Series detects certain essential singularities. On[Series::esss] makes Series generate a message in this case.
• Series can expand about the point x=.
• Series[f,{x,0,n}] constructs Taylor series for any function f according to the formula .
• Series effectively evaluates partial derivatives using D. It assumes that different variables are independent.
• The result of Series is usually a SeriesData object, which you can manipulate with other functions.
• Normal[series] truncates a power series and converts it to a normal expression.
• SeriesCoefficient[series,n] finds the coefficient of the n -order term.

# Examples

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## Basic Examples(3)

Power series for the exponential function around :

 In:= Out= Convert to a normal expression:

 In:= Out= Power series of an arbitrary function around :

 In:= Out= In:= Out= In any operation on series, only appropriate terms are kept:

 In:= Out= ## Possible Issues(7)

Introduced in 1988
(1.0)
|
Updated in 1996
(3.0)