# [Maxima] Test suite failures with cvs version?

Raymond Toy raymond.toy at ericsson.com
Mon Oct 27 16:03:27 CDT 2008

```Dieter Kaiser wrote:
> Hello Ray,
>
> It seems to me that I am a bit tired. Again I was too fast. I did the check for
> conjugate values with different algorithm and not with conjugate values.
>
> Now I arrived at this routine:
>
> (defun expintegral-ei (z)
>   (+
>     (- (expintegral-e 1 (- z)))
> ;    (- (* 0.5 (- (log z) (log (/ 1 z)))) (log (- z)))

I think we need to decide what the value of the above expression is.

For z = -r (r real, r > 0), I have

1/2*(log(z)-log(1/z)) - log(-z)

= 1/2*(log(r)+%i*%pi-log(1/r)-%i*%pi) - log(r)
= 1/2*(2*log(r)) - log(r)
= 0

For all other z = r*exp(%i*theta), maxima says:

1/2*(log(r*exp(%i*theta))-log(1/(r*exp(%i*theta)))-log(-r*exp(%i*theta))\$
rectform(%);
-%i*%pi

This doesn't match what your code does because you sometimes use %i*%pi
or -%i*%pi.

Maybe the real issue is that expintegral_e is computing the wrong value
for negative z?

What definition are you using for Ei and En?

Ray
```