Re: r2.0.6 : bug under Linux ? (+questions on polylog)

[Gerhard Niklasch <nikl@mathematik.tu-muenchen.de>]

In response to
> Message-ID: <XFMail.980329092841.dduparc@club-internet.fr>
> Date: 	Sun, 29 Mar 1998 09:28:41 +0200
> From: dduparc@club-internet.fr

Hello Daniel,
[1.]
> the release 2.0.6 cannot be used by an other user than "root".
> 
> If another user on the system calls gp, he
> (she) receives the error message:
> 
>    ***   unknown user ~/gp
>                        ^__

Try 2.0.7.alpha.  There was a little bug in the tilde expansion
mechanism of which this might be Yet Another Incarnation.  (Its
effect used to depend on the length of the username mod 4, not on
the particular string "root"...)

> 2. Here is a microscopic remark on the documentation:

Noted, with thanks;  will be among numerous other little doc changes
in the next version. :^)

[3.] [...]
> First I would write a correct (complex) evaluation for dilog(),
> then for polylog() or perhaps better for
> multilog(p+1,x) = int_1^x {ln()x^p \over 1-x} dx
> (why not "multilog" ?). [...]
> Of course I should have read the source of PARI on this
> topic! But it is not really litterate programming :-)

Yes, but it's fast because it's written in French, with apologies
to Wieb Bosma for misquoting him. ;)

Do have a glance at src/basemath/trans3.c nevertheless;  it takes
some getting used to, but one _can_ actually read the code.

> Does anibody know a reference for the formulas
> of Zagier in the same paragraph (polylog)?

The paper by Cohen, Lewin and Zagier in the very first issue of
Experimental Mathematics (1992, pp 25-34) might give you some
inspiration.

> [...] a power series with the Bernoulli numbers in
> ln(z), whose convergence is 0< | \ln(z) | < 2 \Pi.

Yes, that's essentially what you'll find in the above paper.
(Plus suggestions for computing zeta values at odd positive
integers, for the other half of the coefficients in the series.)
For very small |z|, you can use the power series in z directly,
and for very large |z|, the functional equation relating dilog(z)
to dilog(1/z).  Don't know about multilog, but since this series
thing for polylog converges very fast, expressing multilog in
terms of one of the polylogs might in fact be appropriate.

Hope this helps, Gerhard