Example: Define a (fake) simplim%function for the generalized Lambert function:
(setf (get '%generalized_lambert_w 'simplim%function) #'(lambda (s v pt) 42)) ;fake
The actual value of limit(generalized_lambert_w(-1,x),x,0,'minus) is minus infinity, but
this calculation doesn't use the services of the simplim%function. Instead, limit assumes
continuity:
(%i93) limit(generalized_lambert_w(-1,x),x,0,'minus);
(%o93) generalized_lambert_w(-1,0)
Appending the simplification generalized_lambert_w(-1,0) --> minf isn't an option because
limit(generalized_lambert_w(-1,x),x,0,'plus) =/= minf (I think, there are other reasons for
not defining this simplification rule.)
For a limit toward inf, the simplim%function is consulted (fake result)
(%i94) limit(generalized_lambert_w(-1,x),x,inf);
(%o94) 42
--Barton