#3994 limits of some gamma_incomplete expressions

[Barton Willis]

I think the true value of this limit is zero:

(%i1) limit(x*gamma_incomplete(1/2,x^2+%i*x),x, inf);

limit: variable must be a symbol or subscripted symbol; found: sin(x)

This similar limit is OK, I think:

(%i14) limit(x*gamma_incomplete(1,x^2+%i*x),x, inf);
(%o14)                                 0

[Barton Willis]

We can make this bug "go away" by changing the call to $limit in gamma-upper-trans to a call to limit-catch

Calling limit-catch is some what different than calling $limit. And maybe the true bug is somewhere else--that is, gamma-upper-trans never should have been called with the arguments that give rise to this bug.

But I think this fix is likely harmless?

(defun gamma-upper-trans (arg func)
  (let ((s (car arg))
    (z (cadr arg)))
    (if (and
     (eq ($sign s) '$pos)
     (zerop1 (limit-catch z (caar tlist) (exp-pt (car tlist)))))
    (taylor2 `((mplus) ((%gamma) ,s)
           ((mtimes) -1 ((%gamma_incomplete_lower) ,s ,z))))
    (taylor2 (diff-expand `((,func) . ,arg)
                  tlist)))))

[Barton Willis]

Better patch is to use the errcatch macro:

(defun gamma-upper-trans (arg func)
  (let ((s (car arg))
    (z (cadr arg)))
    (if (and
     (eq ($sign s) '$pos)
     (zerop1 (car (errcatch ($limit z (caar tlist) (exp-pt (car tlist)))))))
    (taylor2 `((mplus) ((%gamma) ,s)
           ((mtimes) -1 ((%gamma_incomplete_lower) ,s ,z))))
    (taylor2 (diff-expand `((,func) . ,arg)
                  tlist)))))

Thanks to Kris Katterjohn for reminding me about this macro.

[Robert Dodier]

Thanks for working on it, I agree ERRCATCH is a good solution.