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Legendre Polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg56073] Legendre Polynomials
• From: kazimir04 at yahoo.co.uk (Kazimir)
• Date: Thu, 14 Apr 2005 08:56:46 -0400 (EDT)
• References: <d3g8kd$smh$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

> BesselJ[1.5, 0] evaluates to 0 but
> (BesselJ[xx, yyy] /. xx -> 1.5) /. yyy -> 0 evaluates to complex infinity
> 
> I seem to encounter many of these problems with Bessel and Legendre
> functions where I get actual diffrent numerical results depending on
> How I set the parameters.

I worked with Legendre Polynomils and also experienced the problem. If
you use
LegendreP[60, 1.] you have the correct answer 1. It looks like it uses
a smart algorythm. If you use LegendreP[60, x] /. x -> 1. mathematica
first finds the explicit forms of the polynomail, and only afer that
puts x->1. which means that you have to sum up tirms of odre say 10^20
to get 1. Due ti rounding errors you may obtain a wrong answer.