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Re: [Help-gsl] gsl_sf_legendre_Plm_e sign error

From: Robin Hankin
Subject: Re: [Help-gsl] gsl_sf_legendre_Plm_e sign error
Date: Mon, 15 Nov 2004 14:34:01 +0000


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

yes indeed.  I can reproduce the other figures on the page fine.

It seems to me that the curves I get are precise mirror images of
A&S's curves: this would support Gerard Gudman's suggestion (if correct,
this would require only a single typographical error to be present in A&S: the
substitution of $P_{1n}$ for $P^1_n$ in figure 8.2.

One doesn't often hear "Abramovitz and Stegun" and "wrong"
in the same sentence!

best wishes



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 -------

Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
SO14 3ZH
tel +44(0)23-8059-7743
address@hidden (edit in obvious way; spam precaution)

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