bugGNU Octave - Bugs: bug #49129, Legendre polynomials unnecessarily...

 
 

bug #49129: Legendre polynomials unnecessarily restricted to [-1,+1]

Submitted by:  None
Submitted on:  Mon 19 Sep 2016 05:38:11 PM UTC  
 
Category: Octave FunctionSeverity: 1 - Wish
Priority: 3 - LowItem Group: Feature Request
Status: InvalidAssigned to: None
Originator Name: Originator Email: -unavailable-
Open/Closed: ClosedRelease: 4.0.2
Operating System: Microsoft Windows

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Wed 21 Sep 2016 04:19:35 PM UTC, comment #3:

Making a documentation clarification is easy. I did that here (http://hg.savannah.gnu.org/hgweb/octave/rev/ea9df75c9c71).

Rik <rik5>
Project Administrator
Wed 21 Sep 2016 02:54:01 PM UTC, comment #2:

The legendre function does not compute the Legendre poynomials, but the so called "associated Legendre polynomials" (called "associated Legendre functions" in Matlab). They are not polynomials for m odd. All of them are well defined in [-1,1]. For me, the only possible change could be in the documentation, from "Legendre function" to "associated Legendre polynomial" (wikipedia) or "associated Legendre function" (matlab).

Marco Caliari <caliari>
Project Member
Mon 19 Sep 2016 07:54:33 PM UTC, comment #1:

This is possible, although it would introduce an incompatibility with Matlab which restricts the range to [-1, +1] (see http://www.mathworks.com/help/matlab/ref/legendre.html).

There may be ways around the incompatibility. Octave could issue a warning, rather than a full error, if x is outside [-1,+1]. Or there could be a specific warning ID for the legendre function and extended input. By default, this warning ID would be configured to produce an error

But the user could specifically enable an extended input range by using

Just some ideas.

Rik <rik5>
Project Administrator
Mon 19 Sep 2016 05:38:11 PM UTC, original submission:

The legendre function apparently only accepts values of x on the interval [-1,+1]. While this is a documented feature of the function, it is mathematically wrong to restrict the range like this. It is true that, taken as a basis, these function are only orthonormal when restricted to [-1,+1], the functions are just polynomials. They are properly defined on the whole real line. Moreover, there are cases where one wants to evaluate these functions outside of [-1,+1]. This should be supported, if not be default at least optionally.

Anonymous

 

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  • -unavailable- added by caliari (Posted a comment)
  • -unavailable- added by mtmiller (Updated the item)
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    Follow 6 latest changes.

    Date Changed By Updated Field Previous Value => Replaced By
    Wed 10 May 2017 03:11:26 PM UTCcarandraugStatusConfirmed=>Invalid
      Open/ClosedOpen=>Closed
    Tue 20 Sep 2016 05:39:47 PM UTCmtmillerSeverity3 - Normal=>1 - Wish
      Priority5 - Normal=>3 - Low
    Mon 19 Sep 2016 07:54:33 PM UTCrik5Item GroupIncorrect Result=>Feature Request
      StatusNone=>Confirmed

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