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