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Integration anomaly?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127008] Integration anomaly?
  • From: "Szumiloski, John" <john_szumiloski at merck.com>
  • Date: Sat, 23 Jun 2012 04:16:48 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Greetings.

I recently was playing around with the function Log[1 + 1 / ( t^n ) ], and exploring positive values of n.  (I have no interest in nonpositive or complex n)   In particular, I wanted to look at its integral, so I did this: (v8.0.4, Windows XP)


              Integrate[ Log[1+1/(t^n)], { t, 0, Infinity } ]


which gave:

             ConditionalExpression[ -(Pi Csc[Pi/n]), Re[n]<0 ]


Now I am no analysis expert, but it seems pretty clear to me that the integral diverges for negative (real) n.

After doing some further specific symbolic and numeric integrations, I suspect the correct value of this integral is actually


             ConditionalExpression[ Pi Csc[Pi/n], Re[n]>1 ]


although I cannot prove it.

But in any case, the answer Mathematica gave seems clearly wrong.  Can anyone reproduce this (and thus, should someone at WRI look into this), or is my system (or my brain) quirking out?

Thanks,
John  Szumiloski,  Ph.D.

Senior Biometrician
Biometrics Research
WP53B-120
Merck Research Laboratories
P.O. Box 0004
West Point, PA 19486-0004
USA
(215) 652-7346 (PH)
(215) 993-1835 (FAX)
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