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Re: LegendreP & Gauss quad bug

• To: mathgroup at smc.vnet.net
• Subject: [mg25466] Re: [mg25414] LegendreP & Gauss quad bug
• From: BobHanlon at aol.com
• Date: Sun, 1 Oct 2000 02:44:53 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

In a message dated 9/29/2000 1:57:08 AM, cally at kronos.maths.monash.edu.au 
writes:

>There is a bug in the V4 implementation of the Legendre function
>LegendreP, at
>least in the linux version.
>
>I am running Mathematica 4.0 under RedHat 6.2 linux. I have found the
>following bug:
>
>Mathematica 4.0 for Linux
>Copyright 1988-1999 Wolfram Research, Inc.
> -- Motif graphics initialized --
>
>In[1]:= LegendreP[5,2,N[1/3]]
>
>Out[1]= -10.3704
>
>In[2]:= LegendreP[5,2,N[1/3,20]]
>
>Out[2]= -0.17283950617283951
>
>In[3]:= %%/%
>
>Out[3]= 60.
>
>===================================
>
>LegendreP[n,m,x] appears to work properly if x is a machine precision
>number, but if it is higher precision, it gives a result which is out by
>EXACTLY the factor m!/n! This error is NOT present in Version 3.0
>running under Digital Unix.
>

Same results on a Mac. Here is a work around:

LegendreP[5, 2, x] /. (x -> N[1/3, 20])

-10.370370370370370370

Rationalize[%] == LegendreP[5, 2, 1/3]

True

Bob Hanlon