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<title>Issue 701: [tr1] assoc laguerre poly's</title>
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<p><em>This page is a snapshot from the LWG issues list, see the <a href="lwg-active.html">Library Active Issues List</a> for more information and the meaning of <a href="lwg-active.html#NAD">NAD</a> status.</em></p>
<h3 id="701"><a href="lwg-closed.html#701">701</a>. [tr1] assoc laguerre poly's</h3>
<p><b>Section:</b> 5.2.1.1 [tr1::tr.num.sf.Lnm] <b>Status:</b> <a href="lwg-active.html#NAD">NAD</a>
 <b>Submitter:</b> Christopher Crawford <b>Opened:</b> 2007-06-30 <b>Last modified:</b> 2016-02-01</p>
<p><b>Priority: </b>Not Prioritized
</p>
<p><b>View all issues with</b> <a href="lwg-status.html#NAD">NAD</a> status.</p>
<p><b>Discussion:</b></p>
<p>
I see that the definition the associated Laguerre
polynomials 5.2.1.1 [tr1::tr.num.sf.Lnm] has been corrected since
<a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2004/n1687.pdf">N1687</a>.
However, the draft standard only specifies ranks of integer value <code>m</code>,
while the associated Laguerre polynomials are actually valid for real
values of <code>m &gt; -1</code>.  In the case of non-integer values of <code>m</code>, the
definition  <code><i>L</i><sub>n</sub><sup>(m)</sup> = (1/n!)e<sup>x</sup>x<sup>-m</sup> (d/dx)<sup>n</sup> (e<sup>-x</sup>x<sup>m+n</sup>)</code>
must be used, which also holds for integer values of <code>m</code>.  See
Abramowitz &amp; 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 <code>m = +/- 1/2</code> to describe the harmonic
oscillator in 1 dimension, and <code>1/2, 3/2, 5/2, ...</code> in 3
dimensions.
</p>
<p>
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 <code>m</code> or switching the
current ones to <code>double</code>.
</p>

<p><i>[
Batavia (2009-05):
]</i></p>

<blockquote>
<p>
We understand the issue, and have opted not to extend as recommended.
</p>
<p>
Move to NAD.
</p>
</blockquote>


<p id="res-701"><b>Proposed resolution:</b></p>
<p>
</p>





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