Re: [Axiom-developer] Patches

[Martin Rubey]

Waldek Hebisch <address@hidden> writes:

> > But the behaviour is consistent for Gamma, Bessel and Polygamma.  It is not
> > difficult to change this behaviour to leaving the derivative unevaluated,
> > but I'm not sure whether that would really be better.  If you are
> > absolutely sure, please let me know as soon as possible.
> 
> Yes, currently we produce mathematically incorrect result.  In principle user
> may get wrong results even if input does not contain explicit derivative.

Oh? How is that?

> Once we get better support for special functions this may be very serious
> problem.

Probably. By the way: most (probably all) special functions would be covered by
my favourite would-be category/domain hierarchy of differentially algebraic
functions. Then we could say something like

polygamma(a, x)$HOLO(???)

and get the corresponding differential equation.

> I supect that original author did not know how to leave one partial
> derivative unevaluated, while giving value of the second one (ATM this is not
> clear for me either).  If you know how to to this please go on.

OK, I will.

> > How about polygamma?  should D(polygamma(x, x), x) throw an error?  I guess 
> > so.
> > But if we follow you, Bessel* should leave the derivative with respect to 
> > the
> > first argument - i.e., leave it unevaluated.

> polygamma(a, x) has sensible definition also for non-integral a, so just
> leaving D(polygamma(x, x), x) unevaluated is reasonable.

I could not find such a definition.  Could you please send me such a definition
or a reference?

> Since in other places we support only integral a error is reasonable too.
> For Bessel* leaving derivative with respect to the first argument unevaluated
> is preffered to error -- we can still do some calculations with unevaluated
> derivatives.

Yes.

Martin