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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, n_x}, {y, y₀, n_y}]
successively finds series expansions with respect to x, then y.

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[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.

Power series for the exponential function around

Power series of an arbitrary function around