ellsigma(e,z,1)

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

Hi pari-dev,

  this function is documented as:

(18:47) gp > ??ellsigma 

   ellsigma(E,{z = 'x},{flag = 0}):

   Computes  the  value  at z of the Weierstrass sigma function attached to
   [...]
   If flag = 1, computes an arbitrary determination of log(sigma(z)).

Іt's a bit sad that we return something which is not quite well defined
(arbitrary determination), when we could return the value we actually compute,
i.e.

  Log(sigma(z) / z)

which has a nice series expansion. This would also make sense for power
series, while currently

  (18:58) gp > ellsigma(e,z,1)
    ***   at top-level: ellsigma(e,z,1)
    ***                 ^---------------
    *** ellsigma: incorrect type in log(ellsigma) (t_SER).

How about changing this ? To ellsigma(e,z,1) := Log(sigma(z)/z).


We already have analogous quirks for eta (possibly remove the q^(1/24) or
Bessel functions ( e.g. J_nu where the initial (x/2)^nu/Gamma(nu+1) is omitted
since it can't be represented in PARI when nu is not integral ). But here, it
seems to be the more natural definition.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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