#4138 limit((1+1/x)^x,x,6/5) is "und" in complex domain

[Dima Pasechnik]

In complex domain, the above limit is not found:

(%i2) domain;    
(%o2) real
(%i3) limit((1+1/x)^x,x,6/5);
(%o3) %e^((6*log(11/6))/5)
(%i4) domain: complex;
(%o4) complex
(%i5) limit((1+1/x)^x,x,6/5);
(%o5) und
(%i6) limit((1+1/x)^x,x,2/3);
(%o6) %e^((2*log(5/2))/3)

so there are some rational values of x for which this limit works in complex domain, but not for all.
This limit computation is still OK in Maxima 5.45; the bug was discovered while trying to upgrade Maxima in SageMath to the latest version.

~~~-------------------------------------------------------------
Maxima version: "5.46.0"
Maxima build date: "2023-05-05 14:42:03"
Host type: "x86_64-pc-linux-gnu"
Lisp implementation type: "ECL"
Lisp implementation version: "21.2.1"
User dir: "/home/dima/.maxima"
Temp dir: "/tmp"
Object dir: "/home/dima/.maxima/binary/5_46_0/ecl/21_2_1"
Frontend: false
-------------------------------------------------------------

[Barton Willis]

A bit of insight into this bug: Maxima computes the left and right limits OK, but it fails to recognize that the values are the same.

(%i1)   domain : complex$

(%i2)   limit((1+1/x)^x,x,6/5,minus);
(%o2)   11^(6/5)/6^(6/5)

(%i3)   limit((1+1/x)^x,x,6/5,plus);
(%o3)   %e^((6*log(11/6))/5)

Thanks for the bug report.

[Barton Willis]

Fixed by [24a57b] (HEAD, master); appended test to rtest_limit_extra. Closing ticket.