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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.
  • 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=Infinity.
  • Series[f, {x, 0, n}] constructs Taylor series for any function f according to the formula f(0)+f^'(0)x+f^('')(0)x^2/2+...f^((n))(0)x^n/n!.
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Power series for the exponential function around x=0:
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Convert to a normal expression:
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Power series of an arbitrary function around x=a:
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In any operation on series, only appropriate terms are kept:
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