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a tricky limit

  • To: mathgroup at
  • Subject: [mg15327] a tricky limit
  • From: "Arnold Knopfmacher" <arnoldk at>
  • Date: Fri, 8 Jan 1999 04:15:17 -0500
  • Organization: CAM,University ofthe Witwatersrand
  • Sender: owner-wri-mathgroup at

I wish to obtain a numerical estimate (say 8 decimal digits) of the
limit as x  tends to 1 from below of  the function 
h[x]=(Product[(1-fm[x]/(m+1)),{m,2,Infinity}])/(1-x) where
fm[x]=x^(m-m/d) and d is the smallest divisor of m that is greater than
1. The problem is that when I replace Infinity by say 1000 as the upper
limit  of the product, the function blows up near 1. Visual inspection
of the graph of h[x] for 0<x<0.9 say, suggests that the limit should
have a value around 2.1. Can anyone help?

Arnold Knopfmacher
Dept of Computational and Applied Math Witwatersrand University
South Africa

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