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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