#3592 Wrong limit

[Martín-Blas Pérez Pinilla]

This very simple limit:

(%i1) limit((z^(2*n)-1)/(z^2-1),z,-1);
(%o1)                              infinity

goes catastrophically wrong. We can think that a reasonable solution will be

(%i1) declare(n,integer);
(%o1)                                done
(%i2) limit((z^(2*n)-1)/(z^2-1),z,-1);
(%o2)                                  0

And wrong again! BTW all (well, actually I haven't checked all, :-)) the particular cases are correct:

(%i1) limit((z^(2*99)-1)/(z^2-1),z,-1);
(%o1)                                 99

More mystery: the function is even and the other limit

(%i1) limit((z^(2*n)-1)/(z^2-1),z,1);
(%o1)                                  n

Is OK! (even without the declare) Why?

[Robert Dodier]

I see the same behavior, working with Maxima 5.43.0.

[Barton Willis]

Possible fix: When the limit point isn'tinf, apply sratsimp to the first two arguments of lhospital.

What happens, I think, is that when n is an integer, the vanishing expression
((-1) ^n - 1)*((-1)^n + 1) doesn't simplify to zero and that confuses the function lhospital.

Why only apply sratsimp when the limit point isn't an infinity? That's a mystery, but doing so results in limit((-x)*log(%e^x+1)-li[2](-%e^x)+x^2/2,x,inf) returning a nounform, not the correct value of %pi^2/6.

Maybe there is a more logical criteria for applying sratsimp?

(defun lhospital (n d ind)
  (declare (special val lhp?))
   (when (not (infinityp val))  ;proposed fix
      (setq n (sratsimp n)
            d (sratsimp d)))
       ...

[Barton Willis]

Fixed by Commit [37f222], not by the patch I first suggested. This patch fixes the function lhsimp.