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## [Axiom-developer] [#180 bug #9216 differentiating sums with respect to a

 From: kratt6 Subject: [Axiom-developer] [#180 bug #9216 differentiating sums with respect to a bound is wrong] Date: Thu, 23 Jun 2005 05:52:58 -0500

Changes
http://page.axiom-developer.org/zope/mathaction/180Bug9216DifferentiatingSumsWithRespectToABoundIsWrong/diff
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??changed:
-From BillPage Wed Jun 22 13:57:40 -0500 2005
-From: Bill Page
-Date: Wed, 22 Jun 2005 13:57:40 -0500
-Subject: (new) bug #9216 differentiating sums with respect to a bound is wrong
differentiating sums with respect to a bound is wrong

The function $n\mapsto\sum_{k=1}^n f(k,n)$ is well defined only for integral
values of $n$ greater than or equal to zero. There is not even consensus how to
define this function for $n<0$. Thus, it is not differentiable. The fix I
propose is thus

<a href="dvdpatch2.patch">dvdpatch2.patch</a>

??changed:
-+    ddiff l ==
-+      prefix(sub(D::O, third(l)::O), [eval(first(l), second(l), third(l))::O])
-+
-and
-+    setProperty(opdiff, SPECIALDISP, ddiff@(List F -> O) pretend None)
+    ddiff l ==
+      prefix(sub(D::O, third(l)::O), [eval(first(l), second(l),
third(l))::O])
+

and::

+    setProperty(opdiff, SPECIALDISP, ddiff@(List F -> O) pretend None)

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