#2899 Limit that once worked is broken

[kcrisman]

In older Maxima (up to at least 5.24), this command

limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf)

returns 0. Now it doesn't return anything other than itself.

See http://ask.sagemath.org/question/25647/cannot-calculate-limit/ and http://trac.sagemath.org/ticket/17709 for downstream.

[kcrisman]

To be precise, it returns the nounform 'limit((sqrt(n)+1)^n*(sqrt(n+1)+1)^((-n)-1),n,inf)

[kcrisman]

Possibly fixed by Maxima 5.44 - can someone test?

[Kris Katterjohn]

When you say "possibly fixed", does that mean someone sees it returning 0? I'm getting a nounform using git HEAD.

[kcrisman]

"Possibly fixed" because for some reason a function that should use it downstream is returning zero - but thank you for confirming that it is still returning a nounform. (Is that also true if you add domain:complex; before it? We do use a few custom things like that in general.)

[Kris Katterjohn]

I get a nounform either way:

(%i1) domain;
(%o1) real

(%i2) limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf);
(%o2) 'limit((sqrt(n)+1)^n*(sqrt(n+1)+1)^((-n)-1),n,inf)

(%i3) domain:complex$

(%i4) limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf);
(%o4) 'limit((sqrt(n)+1)^n*(sqrt(n+1)+1)^((-n)-1),n,inf)

Maxima version: "branch_5_44_base_83_gdac3edf2c"
Maxima build date: "2020-10-13 08:41:41"
Host type: "x86_64-unknown-openbsd6.7"
Lisp implementation type: "SBCL"
Lisp implementation version: "2.0.1.openbsd"

[Barton Willis]

These bugs are gone in 5.47:

(%i70)  block([domain : complex], limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf));
(%o70)  0
(%i71)  block([domain : real], limit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf));
(%o71)  0
(%i72)  block([domain : complex], tlimit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf));
(%o72)  0
(%i73)  block([domain : real], tlimit((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf));
(%o73)  0
(%i74)  block([domain : complex], gruntz((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf));
(%o74)  0
(%i75)  block([domain : real], gruntz((1+sqrt(n+1))^(-n-1)/(1+sqrt(n))^(-n),n,inf));
(%o75)  0

[kcrisman]

Thanks for the update!

[David Scherfgen]

Closing, as it is fixed.