<p dir="auto"><em>Original ticket <a href="http://projects.scipy.org/scipy/ticket/914" rel="nofollow">http://projects.scipy.org/scipy/ticket/914</a> on 2009-04-06 by trac user lckarssen, assigned to unknown.</em></p>
<p dir="auto">I tried to use special.assoc_laguerre(x,n,k) today and noticed that it returns 0.0 for n=0. However, it should return 1.0 (I used Mathematica to verify as well as a textbook).<br>
Looking at the code, I noticed that special.hyp1f1(a,b,x) which is called by assoc_laguerre() returns 0.0 for a=0, whereas it should return 1.0 (only verified by Mathematica). I tried to look for the code of hyp1f1(), but couldn't find it.</p>
<p dir="auto">Furthermore, I noticed that assoc_laguerre() doesn't have a docstring explaining it's usage. It might be nice to at least point to special.laguerre().</p>
<p dir="auto">The tests were done on a 32bit install of Ubuntu 8.10, which ships scipy 0.6.0</p>
<p dir="auto"><em>Original ticket <a href="http://projects.scipy.org/scipy/ticket/787" rel="nofollow">http://projects.scipy.org/scipy/ticket/787</a> on 2008-11-10 by <a class="user-mention notranslate" data-hovercard-type="user" data-hovercard-url="/users/pv/hovercard" data-octo-click="hovercard-link-click" data-octo-dimensions="link_type:self" href="https://github.com/pv">@pv</a>, assigned to unknown.</em></p>
<p dir="auto">hyp1f1(a=0, b, z) yields infs at points which are poles for a != 0:</p>
<div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="&gt;&gt;&gt; s.hyp1f1(0, -0.99999, 0)
1.0
&gt;&gt;&gt; s.hyp1f1(0, -1, 0)
inf
&gt;&gt;&gt; s.hyp1f1(0, -1.00001, 0)
1.0"><pre class="notranslate"><code class="notranslate">&gt;&gt;&gt; s.hyp1f1(0, -0.99999, 0)
1.0
&gt;&gt;&gt; s.hyp1f1(0, -1, 0)
inf
&gt;&gt;&gt; s.hyp1f1(0, -1.00001, 0)
1.0
</code></pre></div>
<p dir="auto">It would make sense to continue hyp1f1(0, b, z) to unity with all b, z for a=0. See eg. <a href="http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1/03/01/03/0003/" rel="nofollow">http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric1F1/03/01/03/0003/</a> -- this convention is used also by Mathematica.</p>