# [Maxima] Build Failure in Today's CVS

Dieter Kaiser drdieterkaiser at web.de
Fri Dec 26 17:44:17 CST 2008

```Hello Barton,

I do not know much about the taylor code. But I have seen that the trig
functions have the following line in the simplifying function:

((taylorize (mop x) (second x)))

When I add this line to the lambert_w function I get:

(%i9) lambert_w(taylor(x,x,0,5));
(%o9) x-x^2+3*x^3/2-8*x^4/3+125*x^5/24

The only other function I have detected which use the above code is the abs
function. All other function like gamma, bessel, airy, ... do not have this code
and remove the taylor series from the argument.

Is the above expression a correct expansion for lambert_w?

Dieter Kaiser

-----Ursprüngliche Nachricht-----
Von: willisb at unk.edu [mailto:willisb at unk.edu]
Gesendet: Freitag, 26. Dezember 2008 23:36
An: Dieter Kaiser
Cc: ronis at ronispc.chem.mcgill.ca; maxima at math.utexas.edu
Betreff: Re: [Maxima] Build Failure in Today's CVS

The simpcheck converts taylor polynomial inputs to non-taylor polynomials.

OK, but not ideal (current code)

(%i2) lambert_w(taylor(x,x,0,5));
(%o2) lambert_w(x+...)

(%i5) lambert_w(taylor(x,x,0,5));
(%o5) lambert_w(x)

See how the trig functions work (the taylorize function):

(%i6) cos(taylor(x,x,0,5));
(%o6) 1-x^2/2+x^4/24+...

The taylorize code might need to be revisited -- it might
be overly complicated; I haven't looked at it recently.

Barton

```