Returns a specific coefficient from a Taylor series.
SeriesCoefficient[series, n]
SeriesCoefficient[f, {x, x0, n}]
SeriesCoefficient[f, {x, x0, n x}, {y, y0, n y}, …]
SeriesCoefficient[Sin[x], {x, 0, 3}]
→ -1/6SeriesCoefficient[Series[Exp[x], {x, 0, 10}], {x, 0, 5}]
→ 1/120SeriesCoefficient[Exp[x], {x, 0, n}]
→ Piecewise[{{n!^(-1), n >= 0}}, 0]SeriesCoefficient[1/(1 - 2 x), {x, 0, n}]
→ Piecewise[{{2^n, n >= 0}}, 0]SeriesCoefficient[(1 + x)^5, {x, 0, n}]
→ Piecewise[{{Binomial[5, n], Inequality[0, LessEqual, n, LessEqual, 5]}}, 0]SeriesCoefficient[Log[1 + x], {x, 0, n}]
→ Piecewise[{{-((-1)^n/n), n >= 1}}, 0]- Assumptions — default $Assumptions
- Method — default Automatic