
asympt - asymptotic expansions

Calling sequence:
asympt(f, x [ ,n ])
asympt(f, x=v [ ,n ])

Parameters:
f, v   --  expressions
x      --  identifier
n      --  nonnegative integer

Summary:

asympt(f,x=v,n) computes an asymptotic expansion of the expression f
with respect to x at the point v, to order n. The default point is infinity,
and the default order is the value of the global variable ORDER, which is 6
initially.

The function asympt returns a domain object of type gseries that can
be manipulated with the standard arithmetic operations.  The following
methods are available too:  coeff(s, n) gives the coefficient of the n-th
monomial, expr converts the expansion to an expression, removing the error
term, lmonomial gives the leading monomial, lterm gives the leading term,
lcoeff gives the leading coefficient, map maps a function onto the coefficients,

nthterm gives the n-th term, nthmonomial gives the n-th monomial, and
order gives the error term.

____--_>>s-:= asympt(sin(1/x+exp(-x))-sin(1/x),x);

                     - 2           - 4
                    x    exp(- x)   x    exp(- x)     /  - 6         \
           exp(- x) - ------------- + ------------- + O \ x    exp(- x) /
                          2            24

-_>>_-lmonomial( s ), nthterm( s,3 );

                                      - 4
                            exp(- x), x    exp(- x)

-_>>_-t:= asympt( exp(sin(1/x+exp(-exp(x))))-exp(sin(1/x)),x,2);exp(- exp(x))     /  - 2             \

            exp(- exp(x)) + ------------- + O \ x    exp(- exp(x)) /
                               x
           _______     ________
See also:  --_limit_-, --_series_-

