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SeriesCoefficient

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SeriesCoefficient[series, n]

Find the nth coefficient in the given series.

SeriesCoefficient[f, {x, $x_0$, n}]

Find the (x-$x_0$)^n in the expansion of f about the point x=$x_0$.

First we list 5 terms of a series:

• • Series[Exp[Sin[x]], {x, 0, 5}]

Now get the x^4 coefficient:

• • SeriesCoefficient[%, 4]

Do the same thing, but without calling Series first:

• • SeriesCoefficient[Exp[Sin[x]], {x, 0, 4}]

• • SeriesCoefficient[2x, {x, 0, 2}]

• • SeriesCoefficient[SeriesData[x, c, Table[i^2, {i, 10}], 7, 17, 3], 14/3]

• • SeriesCoefficient[SeriesData[x, c, Table[i^2, {i, 10}], 7, 17, 3], 6/3]

• • SeriesCoefficient[SeriesData[x, c, Table[i^2, {i, 10}], 7, 17, 3], 17/3]

See also Series and SeriesData.