[PATCH] Fix assoc_legendre_p(-n,m,x): identically zero
Subject: [PATCH] Fix assoc_legendre_p(-n,m,x): identically zero
From: Kris Katterjohn
Date: Wed, 03 Oct 2012 21:01:34 -0500
Hey everyone,
I've found a bug in assoc_legendre_p(): the results seem to always be zero
when a negative degree is given. For example:
(%i2) assoc_legendre_p(-3,2,1/8);
(%o2) 0
(%i3) assoc_legendre_p(-5,3,1/7);
(%o3) 0
(%i4) assoc_legendre_p(-8,1,1/6);
(%o4) 0
I've created a simple patch to fix this (attached), and created a patch
tracker for it[1]. I think it does The Right Thing.
(%i5) load(orthopoly)$
(%i6) assoc_legendre_p(-3,2,1/8),numer;
(%o6) interval(2.953125, 8.135094160810487E-15)
(%i7) assoc_legendre_p(-5,3,1/7),numer;
(%o7) interval(- 14.54316713060748, 2.376273306325054E-13)
(%i8) assoc_legendre_p(-8,1,1/6),numer;
(%o8) interval(.7000229997231038, 4.669118735062099E-14)
The comments in orthopoly.lisp refer to an equation in A&S relating positive
and negative degrees, but it wasn't actually implemented.
Let me know if there are any problems!
Thanks,
Kris Katterjohn
[1]
https://sourceforge.net/tracker/?func=detail&aid=3574318&group_id=4933&atid=304933
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