Evaluating WeierstrassP at large arguments

*To*: mathgroup at smc.vnet.net*Subject*: [mg120568] Evaluating WeierstrassP at large arguments*From*: "David Park" <djmpark at comcast.net>*Date*: Fri, 29 Jul 2011 04:43:36 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

The WeierstrassP function is doubly periodic. Do the numerical evaluation routines for this function take this into account when evaluating for large arguments, using a Mod function on the argument? If not, would there be something to be gained by the user writing a "front end" for WeierstrassP[z,{g2,g3}] moving z to the principal period parallelogram? Especially if g2 and g3 were fixed and z was scanned only along the direction of one half-period. I'm thinking of something like a high precision mod function followed by a MachinePrecision evaluation of WeierstrassP. My experience has been that calculating the half-periods from g2-g3 has a fair loss of significance but if we only had to calculate them once we could afford extra high precision. David Park djmpark at comcast.net <http://home.comcast.net/~djmpark> http://home.comcast.net/~djmpark/