Series

Series[f, {x, x0, n}]
generates a power series expansion for f about the point to order .

Series[f, {x, x0, nx}, {y, y0, ny}, ...]
successively finds series expansions with respect to x, then y, etc.

Details and OptionsDetails 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 .
  • 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^(th)-order term.

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Power series for the exponential function around :

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Convert to a normal expression:

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Power series of an arbitrary function around :

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

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