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

[anonymous]

URL:
  <http://savannah.gnu.org/bugs/?49129>

                 Summary: Legendre polynomials unnecessarily restricted to
[-1,+1]
                 Project: GNU Octave
            Submitted by: None
            Submitted on: Mon 19 Sep 2016 05:38:11 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 4.0.2
        Operating System: Microsoft Windows

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Details:

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.




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