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taylor - Taylor series expansion

Calling Sequence

taylor(expression, x=a, n)

taylor(expression, x, n)

Parameters

expression

-

expression

x

-

name; independent variable

a

-

realcons; expansion point

n

-

(optional) non-negative integer; expansion order

Basic Information

• 

This help page contains complete information about the taylor command. For basic information on the taylor command, see the taylor help page.

Description

• 

The taylor command computes the order n  Taylor series  expansion of expression, with respect to the variable x, about the point a.

  

If you do not specify the expansion point, a, the Taylor expansion at 0 is returned. This is known as the Maclaurin expansion .

  

If you do not specify the optional argument n, the order of the Taylor expansion returned is the value of the Order environment variable.

• 

The taylor command is a restriction of the more general series command.  For a complete explanation of the parameters, see series.

• 

If the result of the series command applied to the specified arguments is a Taylor series, then this result is returned; otherwise, an error is returned.

• 

To convert a Taylor series to a polynomial, use the convert/polynom command. For more information, see the convert/polynom help page.

Examples

taylorⅇx,x=0,4

1+x+12x2+16x3+Ox4

(1)

taylor1x,x=1,3

1x1+x12+Ox13

(2)

taylorcosx,x=π

1+12xπ2124xπ4+Oxπ6

(3)

taylortanx,x,8

x+13x3+215x5+17315x7+Ox9

(4)

If the expansion point is not specified, the Taylor expansion at 0 is returned.

taylorln1x,x

x12x213x314x415x5+Ox6

(5)

taylorln1x,x=0

x12x213x314x415x5+Ox6

(6)

taylorln1x,x=2

IcsgnIx1π+x212x22+13x2314x24+15x25+Ox26

(7)

taylor1x+y+x3,x=0

Error, does not have a taylor expansion, try series()

series1x+y+x3,x=0

x1+y+x3

(8)

mtaylor1x+y+x3,x=1,y

x15+x14+4x12+2x+y

(9)

By default, the Order environment variable is set to 6. If you do not specify the expansion order, this value is used as the expansion order.

taylorcoshx,x=0

1+12x2+124x4+Ox6

(10)

Order:=10

Order:=10

(11)

∫ⅇx3ⅆx

1312/323x11/3π3Γ23x31/3x11/3Γ13,x3x31/3

(12)

taylor,x=0

x+14x4+114x7+Ox10

(13)

convert,polynom

x+14x4+114x7

(14)

See Also

coeftayl, convert/polynom, Environment Variables, mtaylor, Order, series, taylor, type/realcons, type/taylor


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