Laurent series expansion - Maple Help

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numapprox[laurent] - Laurent series expansion

Calling Sequence

laurent(f, x=a, n)

laurent(f, x, n)

Parameters

f

-

expression representing the function to be expanded

x

-

the variable of expansion

a

-

the point about which to expand

n

-

(optional) non-negative integer stating the order of expansion

Description

• 

The function laurent computes the Laurent series expansion of f, with respect to the variable x, about the point a, up to order n.

• 

The laurent function is a restriction of the more general series function. See series for a complete explanation of the parameters.

• 

If the result of the series function applied to the specified arguments is a Laurent series with finite principal part (i.e. only a finite number of non-negative powers appear in the series) then this result is returned; otherwise, an error-return occurs.

• 

The command with(numapprox,laurent) allows the use of the abbreviated form of this command.

Examples

withnumapprox:

laurent1xsinx,x=0

x2+16+7360x2+Ox4

(1)

laurentΓx,x,2

x1γ+112π2+12γ2x+Ox2

(2)

r:=x2+2x3x411x3+42x268x+40

r:=x2+2x3x411x3+42x268x+40

(3)

laurentr,x=2

53x23239x223227x21328132243x232729x22+Ox23

(4)

See Also

series, taylor, type[laurent]


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