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### 701. [tr1] assoc laguerre poly's

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

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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: