Re: [Reduce-algebra-developers] expansion of gamma function

[Rainer S. <rai...@gm...>]

On Fri, 9 Oct 2015 at 23:58 +0600, Andrey G. Grozin wrote:

 > grozin@dns ~/reduce-3235 $ bin/rfpsl
 > Redfront 3.2, built 09-Oct-2015 ...
 > Loading image file: 
 > /home/grozin/reduce-3235/pslbuild/x86_64-unknown-gentoo2.2/red/reduce.img
 > 
 > Reduce (Free PSL version),  9-Oct-2015 ...
 > 
 > 1: load_package specfn;
 > 
 > 2: load_package tps;
 > 
 > 3: psexplim 5$
 > 
 > 4: ps(gamma(1+x),x,0);
 > ***** `polygamma_aux' is an undefined function
 > 
 > 5:
 > 
 > What can polygamma_aux be?

polygamma_aux is an internal function in the package sfgamma, used for computing 
the value of the polygamma function for integer argument.

sfgamma it should be loaded automatically, and I will checkin a correction for 
that. If you load this package by hand, you see the effect that Alan described:

4: load_package sfgamma;

5: ps(gamma(1+x),x,0);

***** Recursion too deep in ps!:unknown!-crule 

 > I seem to remember that in elder days this expansion worked (though I 
 > may be wrong).

Something similar happens with the taylor package: It tries to compute the 
taylor series be differentiation, but 

df(gamma(x+1),x);

gives

 gamma(x + 1)*(psi(x)*x + 1)
-----------------------------
              x

which leads to computation of psi(0) and therefore to an error.


  Rainer