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Re: [Help-gsl] gsl_sf_legendre_Plm_e sign error

From: Brian Gough
Subject: Re: [Help-gsl] gsl_sf_legendre_Plm_e sign error
Date: Mon, 15 Nov 2004 13:24:44 +0000

Robin Hankin writes:
 > I'm working with Legendre functions and I'm trying to reproduce 
 > Abramowitz and Stegun's
 > figure 8.2 which shows $P^1_n(x)$.

The figure in Abramowitz and Stegun is wrong (compare with
8.6.1)---the value from GSL is correct.


Brian Gough

Network Theory Ltd,
Commercial support for GSL ---

------- start of forwarded message -------
From: Gerard Jungman <address@hidden>
To: Brian Gough <address@hidden>
Subject: Re: legendre bug?
Date: Fri, 12 Nov 2004 15:57:39 -0700

On Thu, 2004-11-11 at 10:08, Brian Gough wrote:
> Hello,
> P_1^1(0) should be 1 I think.
> See

If you apply A+S 8.6.1, you get -1. This is consistent
with everything I have seen before as well. The function
legendre_Pmm() in legendre_poly.c implements a standard
formula for this. I'm not sure what A+S thought
they were plotting, but it is not what they say.

They may actually have plotted what they call P_{mm}, with
both indices downstairs. See the Notation section at the
very beginning of chapter 8.

I can't find the original email (from R. Hankin),
but maybe you have it and can forward this response
to him and/or the list.

Gerard Jungman <address@hidden>
Los Alamos National Laboratory

------- end of forwarded message -------

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