asympt
asymptotic expansion
Calling Sequence
Parameters
Description
Examples
Compatibility
asympt(f, x)
asympt(f, x, n)
f
-
algebraic expression in x
x
name
n
positive integer (truncation order)
oterm
(optional) truefalse
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.
If the optional argument oterm=false is given, then convert(result,polynom) is applied before returning.
asymptx1−x−x2,x
−1x+1x2−2x3+3x4−5x5+O1x6
asymptn!sqrt2π,n,3
11n+1n12+1n32288+O1n521nnⅇn
asymptexpx21−erfx,x
1πx−12πx3+34πx5+O1x7
asymptsqrtπ2BesselJ0,x,x,3
sinx+π41x−cosx+π41x328−9sinx+π41x52128+O1x72
serieslnxx−1,x,8
−lnx−lnxx−lnxx2−lnxx3−lnxx4−lnxx5−lnxx6−lnxx7+Ox8
asymptlnxx−1,x,8
lnxx+lnxx2+lnxx3+lnxx4+lnxx5+lnxx6+lnxx7+O1x8
asymptlnxx−1,x,8,oterm=false
lnxx+lnxx2+lnxx3+lnxx4+lnxx5+lnxx6+lnxx7
The asympt command was updated in Maple 2016; see Advanced Math.
The asympt command was updated in Maple 2024.
The oterm option was introduced in Maple 2024.
For more information on Maple 2024 changes, see Updates in Maple 2024.
See Also
limit
series
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