Re: Problem with Infinite products

• To: mathgroup at smc.vnet.net
• Subject: [mg65318] Re: Problem with Infinite products
• From: Roger Bagula <rlbagulatftn at yahoo.com>
• Date: Sun, 26 Mar 2006 05:44:01 -0500 (EST)
• References: <dvrbsp\$a3a\$1@smc.vnet.net> <e035oq\$2d8\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Maxim Rytin,
Actually does run better,

Clear[f, zta]
f[n_Integer?Positive, 1] := If[Mod[Prime[n], 12] - 1 == 0, Prime[n], 1/2]
f[n_Integer?Positive, 2] := If[Mod[Prime[n], 12] - 5 == 0, Prime[n], 1/2]
f[n_Integer?Positive, 3] := If[Mod[Prime[n], 12] - 7 == 0, Prime[n], 1/2]
f[n_Integer?Positive, 4] := If[Mod[Prime[n], 12] - 11 == 0, Prime[n], 1/2]
zta[x_, m_] := Module[{n}, Product[f[n, m]^(x)/(-1 + f[n, m]^(x)), {n, 1,
Infinity}]]
zta[2, 1]
N[%]
zta[2, 2]
N[%]
zta[2, 3]
N[%]
zta[2, 4]
N[%]
N[Product[zta[2, n], {n, 1, 4}]/Zeta[2]]
Maxim wrote:

>
> zta[x_, m_] := Module[{n},
>    Product[f[n, m]^(x)/(-1 + f[n, m]^(x)), {n, 1, Infinity}]]
>
> Then Product[zta[2, n], {n, 1, 4}] won't evaluate to zero.
>
> Maxim Rytin
> m.r at inbox.ru
>

```

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