Series Expansions

Power series are in many ways the algebraic analog of limited-precision numbers. The Wolfram Language can generate series approximations to virtually any combination of built-in mathematical functions. It will then automatically combine series, truncating to the correct order. The Wolfram Language supports not only ordinary power series, but also Laurent series and Puiseux series, as well as complex asymptotic expansions for special functions with elaborate branch cut structures. Many of the formulas used are original to the Wolfram Language.

Series construct a series expansion in one or more variables

Normal convert from a series expansion to an ordinary expression

O symbolic representation of a higher-order series term

Assumptions, Assuming give assumptions about parameters

Coefficient coefficient of a particular term in an ordinary power series

CoefficientList coefficients in an ordinary power series

SeriesCoefficient coefficient of a term in a general series

InverseSeries find the functional inverse of a series

ComposeSeries find the functional composition of series

Limit find the limit of a series at its expansion point

Integrate integrate a series

D differentiate a series

LogicalExpand expand out equations for series

PadeApproximant construct a rational approximation to a function