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asympt

asymptotic expansion

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

asympt(f, x)

asympt(f, x, n)

Parameters

f

-

algebraic expression in x

x

-

name

n

-

positive integer (truncation order)

Description

• 

The function asympt computes the asymptotic expansion of f with respect to the variable x (as x approaches infinity).

• 

The third argument n specifies the truncation order of the series expansion.  If no third argument is given, the value of the global variable Order (default Order = 6) is used.

• 

Specifically, asympt is defined in terms of the series function

subsx=1x,seriessubsx=1x,f,x=0,n

  

However, the expression returned will be in sum-of-products form rather than in the series form.

Examples

asymptx1xx2,x

1x+1x22x3+3x45x5+O1x6

(1)

asymptn!2Pi,n,3

11n+1n12+1n32288+O1n521nnⅇn

(2)

asymptⅇx21erfx,x

1πx12πx3+34πx5+O1x7

(3)

asymptPi2BesselJ0,x,x,3

sinx+π41xcosx+π41x3289sinx+π41x52128+O1x72

(4)

serieslnxx1,x,8

lnxlnxxlnxx2lnxx3lnxx4lnxx5lnxx6lnxx7+Ox8

(5)

asymptlnxx1,x,8

lnxx+lnxx2+lnxx3+lnxx4+lnxx5+lnxx6+lnxx7+O1x8

(6)

Compatibility

• 

The asympt command was updated in Maple 2016; see Advanced Math.

See Also

limit

series