[Maxima-bugs] [maxima:bugs] #4276 expintegral_ei incorrect behavior at infinity

[Dan G. <dg...@us...>]

- **status**: open --> closed
- **assigned_to**: Dan Gildea
- **Comment**:

Fixed by [76f95cbc5c96ea55c888160279305b4e41d37e4d]



---

**[bugs:#4276] expintegral_ei incorrect behavior at infinity**

**Status:** closed
**Group:** None
**Labels:** taylor expintegral_ei limit 
**Created:** Thu Mar 21, 2024 09:08 PM UTC by opfromthestart
**Last Updated:** Mon Mar 25, 2024 07:52 PM UTC
**Owner:** Dan Gildea


Some behavior of expintegral_ei is not correct 
```
(%i25) limit(((expintegral_ei(x)/%e^x)*x-1)*x,x,inf);
(%o25)                               minf
```

Bu this limit is known to be 1 (eg `https://www.wolframalpha.com/input?i=limit+x+to+infinity+%28%28Ei%28x%29%2Fe%5Ex%29*x-1%29*x`).

```
(%i29) taylor(expintegral_ei(x)*%e^-x,x,inf,10);

taylor: encountered an unfamiliar singularity in:
expintegral_ei(x)
 -- an error. To debug this try: debugmode(true);
```
But this Laurent series can be found (`https://www.wolframalpha.com/input?i=Ei%28x%29e%5E-x+series+at+infinity`).
```
Maxima version: "5.45.1"
Maxima build date: "2021-12-06 23:50:08"
Host type: "x86_64-pc-linux-gnu"
Lisp implementation type: "GNU Common Lisp (GCL)"
Lisp implementation version: "GCL 2.6.12"
User dir: "/home/opfromthestart/.maxima"
Temp dir: "/tmp"
Object dir: "/home/opfromthestart/.maxima/binary/5_45_1/gcl/GCL_2_6_12"
Frontend: false
```
I also have tried it on 5.47.0 and I get the same errors.


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