dduparc on Sun, 29 Mar 1998 12:59:44 +0200

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thanks to Gerhard

Dear Gerhard, dear friends lovers of PARI-GP,

Thank you very much.

(Sorry not to speak German, and
badly English. However I do speak French but I am 
quite slow (doing math, programming, etc... :-) 

That's exactly what i wanted.

However I tried to read trans3.c but I did'nt understand
(for instance) the use of -ln(-ln(-z))). There are
some curiosities in the arrangement of the different
functions involved. For example, in polylog() which is normally
called by by gpolylog() there is some code for the case m<=0.
However this case is treated by gpolylog() in case of numeric
evaluation. That's fine since polylog() returns
 -1/2 when m=0 (gneg(ghalf))(??). Thus polylog() is called
by other functions with non numeric arguments (GEN)(??).

I must apologize: "multilog"(p,z) = \int_1^z {ln(t)^{p-1}\over 1-t} dt
is the *only* function having some relation with polylog() being
not named in Lewin's book (with the exception of the Clausen
function \Lambda which is closely related). 
So i named it multilog() for simplicity: this function may be interesting 
in vue of the writing an extension of an engine of integration,
as in MuPAD. The case p=2, i.e dilog() is  completly  achieved 
in Maple V.4. I have the project (you boaster, Duparc ;-) to extend
the integration engine of MuPAD to dilog() then perhaps multilog()
in order to test some accelerators of convergence to the values
of polylog() or multilog().

[end of noise]
Best regards.

Daniel Duparc <dduparc@club-internet.fr>
29 av. de la Commune de Paris
94400 Vitry sur Seine (France)