SOLUTIONS

Series Expansions
Power series are in many ways the algebraic analog of limitedprecision numbers. Mathematica can generate series approximations to virtually any combination of builtin mathematical functions. It will then automatically combine series, truncating to the correct order. Mathematica 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 Mathematica.
ReferenceReference
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 higherorder 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