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one more bug?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31657] one more bug?
*From*: Otto Linsuain <linsuain at andrew.cmu.edu>
*Date*: Fri, 23 Nov 2001 05:46:31 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
It looks like there is a bug either when integrating or when representing
the Log. In short Mathematica seems to understand that
Log[1/u]==-Log[u], when 0 < u <1, for example.
Although this is not true in general because of the issue with the branch
cut, and Mathematica will not yield True for this question. But if the
assumption is given that 0 < u < 1, then Mathematica happily obliges and
answers True. Plotting these two on the interval [0,1] also yield
identical graphs (rather I plot 1/Sqrt[Log[1/u]]). Integrating these
functions from zero to one gives opposite answers! (Sqrt[Pi] and
-Sqrt[Pi]). The positive answer is the correct one! (see attachment)
[Contact the author to get the attachment - moderator]
Upon closer examination it looks like the culprit is the Sqrt. I get
equally contradictory answers for the integrals of Sqrt[Log[1/u]] and
Sqrt[-Log[u]], but no problem with the integrals of Log[1/u] and -Log[u].
All these integrals, by the way, are convergent and perfectly well
defined.
Otto Linsuain
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