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MathGroup Archive 2005

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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
> 
> 


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