[Maxima-bugs] [maxima:bugs] Re: #4758 limits of the form gamma(ind)

[Stavros M. <mac...@us...>]

Re "the current scheme of converting to factorial form", it does produce some strange results, but it simplifies the code compared to handling **gamma** and **!** separately.

The original sin is of course supporting two distinct functions. But they are not handled symmetrically. For example, there is **minfactorial** but no **mingamma**, so you need to do something like **makegamma(minfactorial(makefact(ex)))**. But **gammalim** doesn't apply to **factorial**. **makegamma** works on **pochhammer**, and **makefactorial** doesn't. But **pochhammer(1,x)** returns **x!** and not **gamma(x+1)**. **stirling** works on **gamma** but not **!**.

Presumably some users prefer one and others prefer the other. (I hope that no real users (as opposed to perverse testers like you and me) write expressions like **x!/gamma(x)**.) This is different from **sin** and **cos**, where they are invariably used together, even though they are related in a similar way.

The "obvious" solution is to use one of them universally as the *internal representation*, and only support the other as an input/output form, perhaps under the control of a switch, e.g., **show_gammafact**. So with **show_gammafact=factorial**, **gamma(x)** would display as **(x-1)!**.

We could  even set that variable when the user enters one or the other, but that might be more and not less confusing for users....

All this to say that it's not a **limit** problem.




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**[bugs:#4758] limits of the form gamma\(ind\)**

**Status:** open
**Group:** None
**Labels:** limit gamma 
**Created:** Sat Jun 06, 2026 06:55 PM UTC by Barton Willis
**Last Updated:** Sat Jun 06, 2026 09:34 PM UTC
**Owner:** nobody


Should be `ind`, not `und`:

~~~
(%i1)	limit(gamma(4+sin(x)),x,inf);
(%o1)	und
~~~

Related bug:  should be 0, not `und`
~~~
(%i2)	limit(gamma(4+sin(x))/x,x,inf);
(%o2)	und
~~~


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