Re: LegendreP error (bug?) in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg59084] Re: LegendreP error (bug?) in Mathematica*From*: "sashap" <pavlyk at gmail.com>*Date*: Thu, 28 Jul 2005 02:27:27 -0400 (EDT)*References*: <dbq2o2$713$1@smc.vnet.net><dbt3bk$sib$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

To symbio: Differential equation for LegendreP has the symmetry n->(-n-1). This symmetry is used to define what we mean by LegendreP[n,x] for negative n. The formula is quoted in my previous email. In the previous post I must have added that the sum does not define LegendreP for negative n. Per your suggestion I am quoting you the result from a math book, which says: LegendreP[n, 1] == 1 for non-negative integer n LegendreP[n,1] == LegendreP[ -n-1, 1] == 1 for nagative integer n. Please feel free to quote the text-book you refer to, to be more precise. I am using N.N. Lebedev, "Special Functions and Their applications" Oleksandr Pavlyk Wolfram Research