• ← RootSum
• → SeriesCoefficient

Series

WMA link

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

Represents the series expansion around x=$x_0$ up to order n.

For elementary expressions, Series returns the explicit power series as a SeriesData expression:

• • series = Series[Exp[x^2], {x,0,2}]

The expression created is a SeriesData object:

• • series // FullForm

Replacing x with does a value produces another SeriesData object:

• • series /. x->4

Normal transforms a SeriesData expression into a polynomial:

• • series // Normal

• • (series // Normal) /. x-> 4

• • Clear[series];

We can also expand over multiple variables:

• • Series[Exp[x-y], {x, 0, 2}, {y, 0, 2}]

See also SeriesCoefficient and SeriesData.