Re: Product {for p=2 to infinity} (p^2+1)/(p^2-1) version=3.0.2
- To: mathgroup at smc.vnet.net
- Subject: [mg53953] Re: [mg53937] Product {for p=2 to infinity} (p^2+1)/(p^2-1) version=3.0.2
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 5 Feb 2005 03:15:09 -0500 (EST)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
Product[(p^2+1)/(p^2-1), {p, 2,Infinity}]//FullSimplify Sinh[Pi]/Pi %//N 3.67608 Verify result: ListPlot[Table[{m,Product[(p^2+1)/(p^2-1), {p, 2,m}]},{m,5,150,5}], PlotJoined->True]; Table[Product[(p^2+1)/(p^2-1), {p, 2,m}],{m,5,200,5}] == Table[Times@@Table[(p^2+1)/(p^2-1), {p, 2,m}],{m,5,200,5}] True Bob Hanlon > > From: seidovzf at yahoo.com (Zak Seidov) To: mathgroup at smc.vnet.net > Date: 2005/02/04 Fri AM 04:12:17 EST > To: mathgroup at smc.vnet.net > Subject: [mg53953] [mg53937] Product {for p=2 to infinity} (p^2+1)/(p^2-1) > > Dear Math gurus, > I try to copy Math session: > \!\(FullSimplify[\[Product]\+\(p = 2\)\%\[Infinity]\((\(p\^2 + > 1\)\/\(p\^2 - \1\))\)] > n Sinh[\[Pi]]\/\[Pi]\), > that is, > Product {for p=2 to infinity} (p^2+1)/(p^2-1)=> > sinh(pi)/pi=3.67608 - > is it OK, > or this should be 3/2? > Please email me your help: > seidovzf at yahoo.com > > Many thanks, > Zak > >