Series

Computes a power series expansion.

Independently checkable: an answer for this function is re-derived by a different route and compared - the workbench and the verify tool do this automatically, so a wrong answer is caught rather than trusted. History →

Forms

Series[f, {x, x0, n}]

Series[f, x -> x0]

Series[f, {x, x0, n x}, {y, y0, n y}, …]

Verified examplesSeries[Exp[x], {x, 0, 4}] → SeriesData[x, 0, {1, 1, 1/2, 1/6, 1/24}, 0, 5, 1]Series[1 + x, {x, 0, 3}] → SeriesData[x, 0, {1, 1}, 0, 4, 1]Series[x^2 + x^4, {x, 0, 7}] → SeriesData[x, 0, {1, 0, 1}, 2, 8, 1]Series[3, {x, 0, 3}] → 3 Series[a + b, {x, 0, 3}] → a + b Series[1/(1 + x), {x, Infinity, 3}] → SeriesData[x, Infinity, {1, -1, 1}, 1, 4, 1]Normal[Series[Sqrt[x^2 + 1], {x, Infinity, 2}]] → 1/(2*x) + xOptions

Analytic — default True
Assumptions — default $Assumptions
SeriesTermGoal — default Automatic

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Used in

Asymptotic behavior of a function - 4 steps

Topics

Analytic Number Theory - Operations
Asymptotics - Asymptotic Solvers
Calculus - Vector Calculus »
Elementary Functions - Hyperbolic Functions »
Formula Manipulation - Extracting Parts of Formulas
Manipulating Equations - General

Used in

Topics

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