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Section: 5.2.1.1 [tr1::tr.num.sf.Lnm] Status: NAD Submitter: Christopher Crawford Opened: 2007-06-30 Last modified: 2016-02-01
Priority: Not Prioritized
View all issues with NAD status.
Discussion:
I see that the definition the associated Laguerre
polynomials 5.2.1.1 [tr1::tr.num.sf.Lnm] has been corrected since
N1687.
However, the draft standard only specifies ranks of integer value m,
while the associated Laguerre polynomials are actually valid for real
values of m > -1. In the case of non-integer values of m, the
definition Ln(m) = (1/n!)exx-m (d/dx)n (e-xxm+n)
must be used, which also holds for integer values of m. See
Abramowitz & Stegun, 22.11.6 for the general case, and 22.5.16-17 for
the integer case. In fact fractional values are most commonly used in
physics, for example to m = +/- 1/2 to describe the harmonic
oscillator in 1 dimension, and 1/2, 3/2, 5/2, ... in 3
dimensions.
If I am correct, the calculation of the more general case is no
more difficult, and is in fact the function implemented in the GNU
Scientific Library. I would urge you to consider upgrading the
standard, either adding extra functions for real m or switching the
current ones to double.
[ Batavia (2009-05): ]
We understand the issue, and have opted not to extend as recommended.
Move to NAD.
Proposed resolution: