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A080729
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Decimal expansion of the infinite product of zeta functions for even arguments.
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2
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1, 8, 2, 1, 0, 1, 7, 4, 5, 1, 4, 9, 9, 2, 9, 2, 3, 9, 0, 4, 0, 6, 7, 2, 5, 1, 3, 2, 2, 2, 6, 0, 0, 6, 8, 4, 8, 5, 7, 8, 2, 6, 8, 0, 2, 8, 6, 4, 8, 2, 7, 1, 7, 5, 5, 0, 0, 2, 0, 9, 3, 8, 0, 0, 2, 8, 6, 0, 6, 5, 8, 8, 6, 7, 7, 0, 5, 4, 8, 8, 9, 3, 6, 3, 9, 6, 0, 2, 4, 9, 7, 5, 2, 1, 4, 5, 2, 9, 7, 6, 6, 1, 0, 9, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Eric Weisstein's World of Mathematics, Abelian group.
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FORMULA
| Decimal expansion of zeta(2)*zeta(4)*...*zeta(2k)*...
If u(k) denotes the number of Abelian groups with group order k, then prod(k>=1, zeta(2*k))=sum(k>=1, u(k)/k^2). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 25 2003
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EXAMPLE
| The value to 39 decimal places (calculated by Mathematica) is 1.82101745149929239040672513222600684857...
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MATHEMATICA
| RealDigits[Product[Zeta[2n], {n, 500}], 10, 110][[1]] (* From Harvey P. Dale, Jan 31 2012 *)
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CROSSREFS
| Cf. A021002, A080730.
Sequence in context: A098829 A190404 A114314 * A164800 A011008 A010149
Adjacent sequences: A080726 A080727 A080728 * A080730 A080731 A080732
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KEYWORD
| cons,nonn,changed
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AUTHOR
| Deepak R. N (deepak_rn(AT)safe-mail.net), Mar 08 2003
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EXTENSIONS
| More terms from Benoit Cloitre, Mar 08, 2003
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