[CIG-MC] CitcomS Legendre polynomial normalization

Shijie Zhong Shijie.Zhong at Colorado.Edu
Wed Mar 3 21:06:41 PST 2010

I do not have a reference for the recursion relationship used in CitcomS. I will 
see whether I can find my original notes for this. The troubles with the standard 
form and the code provided in Numerical Recipes were related to calculations of  
factorials in the numerator and denominator -- for relatively large L, the 
factorials would blow up even in double precision. 

Shijie Zhong
Department of Physics
University of Colorado at Boulder
Boulder, CO 80309
Tel: 303-735-5095; Fax: 303-492-7935
Web: http://anquetil.colorado.edu/szhong

---- Original message ----
>Date: Wed, 3 Mar 2010 17:26:21 -0800
>From: Magali Billen <mibillen at ucdavis.edu>  
>Subject: Re: [CIG-MC] CitcomS Legendre polynomial normalization  
>To: Shijie Zhong <Shijie.Zhong at Colorado.Edu>
>Cc: "Joy Hines" <jmhines at ucdavis.edu>,cig-mc at geodynamics.org
>   Hello Shijie,
>   Yes, its the factors in the recursion relationship
>   that we were surprised to find, as the rest the 
>   recursion relationship steps are the same as that in
>   Numerical recipes...I'm glad to know that this
>   is stable for large L as we'll be going up to about
>   L=360. Any chance that there's a reference
>   for the recursion relationship (or maybe point us in
>   the right direction, we've looked up several others
>   and haven't found the same thing)? No hurry, but it
>   seems like this is a good thing to have reference
>   for general
>   CitcomS background information too.
>   Thanks for answering our e-mail so quickly,
>   Magali
>   On Mar 3, 2010, at 5:13 PM, Shijie Zhong wrote:
>     You are right that the recursion relation for the
>     Legendre polynomials used in 
>     CitcomS is different from the standard in
>     Numerical Recipes by Press. The 
>     standard one in Numerical Recipes blows up for
>     spherical harmonic degree l > 
>     20 or something, even with double precision
>     computation. I re-derived a 
>     recursion relation in 1997 that is stable for
>     nearly all l's and is used in CitcomS. 
>   -----------------------------
>   Associate Professor, U.C. Davis
>   Department of Geology/KeckCAVEs
>   Earth & Physical Sciences Bldg, rm 2129
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