a tricky limit
- To: mathgroup at smc.vnet.net
- Subject: [mg15327] a tricky limit
- From: "Arnold Knopfmacher" <arnoldk at gauss.cam.wits.ac.za>
- Date: Fri, 8 Jan 1999 04:15:17 -0500
- Organization: CAM,University ofthe Witwatersrand
- Sender: owner-wri-mathgroup at wolfram.com
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?
Thanks
Arnold Knopfmacher
Dept of Computational and Applied Math Witwatersrand University
South Africa
- Follow-Ups:
- Re: a tricky limit
- From: Jurgen Tischer <jtischer@col2.telecom.com.co>
- Re: a tricky limit
- From: Daniel Lichtblau <danl>
- Re: a tricky limit