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 1.5.9 and Section 3.6.1.
Implementation Notes: see section A.9.5.
See also: InverseSeries, ComposeSeries, Limit, Normal, InverseZTransform.
Related packages: Calculus`Pade`, NumericalMath`Approximations`, DiscreteMath`RSolve`.