Karim Belabas on Thu, 13 Feb 2014 19:13:43 +0100 |
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ellsigma(e,z,1) |
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] `