limits involving acosh: strange question

Computer Algebra System written in Common Lisp

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#5201 limits involving acosh: strange question

Milestone: None

Status: closed

Owner: nobody

Labels: limit (212) acosh (8)

Priority: 5

Updated: 2026-09-02

Created: 2026-09-01

Creator: David Scherfgen

Private: No

This asks a strange question:

(%i1) limit((acosh(-1+x)-acosh(-1))/x, x, 0);
Is acosh(- 1) positive or zero?

Discussion

Viktor Toth - 2026-09-01

This one (the first case) caught my attention because I am now wondering if it is a recent regression?

Maxima 5.50.0 https://maxima.sourceforge.io using Lisp GNU Common Lisp (GCL) GCL 2.7.1 git tag Version_2_7_2ore5 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) limit((acosh(-1+x)-acosh(-1))/x, x, 0); (%o1) infinity

But yes, the second case fails with indefinite recursion in 5.50.
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- David Scherfgen - 2026-09-01
  
  Yes, it's recent. The question is asked by ratlim. A recent commit made ratlim ask questions instead of "guessing" and returning a potentially wrong result, and it seems like this is caused by it. I will look into it.
  
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David Scherfgen - 2026-09-02

summary: limits involving acosh: strange question and infinite recursion --> limits involving acosh: strange question

Description has changed:

Diff:

--- old +++ new @@ -3,8 +3,3 @@ (%i1) limit((acosh(-1+x)-acosh(-1))/x, x, 0); Is acosh(- 1) positive or zero? ~~~ - -This seems to recurse infinitely: -~~~ -(%i2) limit((acosh(-2+%i/2+x)-acosh(-2+%i/2))/x, x, 0); -~~~
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David Scherfgen - 2026-09-02

Splitting this because they're two unrelated bugs.

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David Scherfgen - 2026-09-02

status: open --> closed
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David Scherfgen - 2026-09-02

The question-asking bug has been fixed by commit [e13bf5]. The other one is now #5214 and seems to be more difficult to fix.

Related

Commit: [e13bf5]

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