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 Documentation / Mathematica / Built-in Functions / Algebraic Computation / Calculus  /
Series

  • Series[ f , x , , n ] generates a power series expansion for f about the point to order .
  • Series[ f , x , , , y , , ] successively finds series expansions with respect to y, then x.
  • Series can construct standard Taylor series, as well as certain expansions involving negative powers, fractional powers and logarithms.
  • Series detects certain essential singularities.
  • Series can expand about the point .
  • 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 order term.
  • See the Mathematica book: Section 1.5.9Section 3.6.1.
  • See also Implementation NotesA.9.55.17MainBookLinkOldButtonDataA.9.55.17.
  • See also: InverseSeries, ComposeSeries, Limit, Normal.
  • Related packages: Calculus`Pade`, NumericalMath`Approximations`, DiscreteMath`RSolve`.

    Further Examples

    This gives the general Taylor series up to the fifth degree term for a function f.

    In[1]:=

    Out[1]=

    Here is a series for .

    In[2]:=

    Out[2]=

    You can do arithmetic on series objects.

    In[3]:=

    Out[3]=

    This gives a series for a function of two variables.

    In[4]:=

    Out[4]=