Re: [Help-gsl] gsl_sf_legendre_Plm_e sign error

[Robin Hankin]

Hi


> 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

Robin







> --
> regards
>
> Brian Gough
>
> Network Theory Ltd,
> Commercial support for GSL --- http://www.network-theory.co.uk/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 http://lists.gnu.org/archive/html/help-gsl/2004-11/msg00011.html
>
> 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)