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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:** 2016-02-10

**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 *L*_{n}^{(m)} = (1/n!)e^{x}x^{-m} (d/dx)^{n} (e^{-x}x^{m+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:**