Next: References Up: No Title Previous: Examples from definite

Examples of asymptotic series and limits.

Maple includes an implementation of a new model of ``hierarchical'' series in which various essential singularities in addition to simple poles are allowed e.g. and about . For example, the asymptotic series for the error function is


  > asympt(erf(x),x);

From this series expansion, Maple can determine the following limit


  > Limit(exp(x^2)*(1-erf(x)),x=infinity) =
  > limit(exp(x^2)*(1-erf(x)),x=infinity);

Release 2 includes a more powerful model of series for nested functions. For example, the limit of the nested function below


  > f := (GAMMA(n+1/GAMMA(n))-GAMMA(n))/ln(n):
  > Limit(f,n=infinity) = limit(f,n=infinity);


Klaus Steinberger
Mi Apr 13 10:02:38 MDT 1994