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.