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A080729 Decimal expansion of the infinite product of zeta functions for even arguments. 3
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; text; internal format)
OFFSET
1,2
LINKS
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 658.
Eric Weisstein's World of Mathematics, Abelian group.
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, Jun 25 2003
EXAMPLE
The value to 39 decimal places (calculated by Mathematica) is 1.82101745149929239040672513222600684857...
MATHEMATICA
RealDigits[Product[Zeta[2n], {n, 500}], 10, 110][[1]] (* Harvey P. Dale, Jan 31 2012 *)
CROSSREFS
Sequence in context: A098829 A190404 A243433 * A262080 A164800 A011008
KEYWORD
cons,nonn
AUTHOR
Deepak R. N (deepak_rn(AT)safe-mail.net), Mar 08 2003
EXTENSIONS
More terms from Benoit Cloitre, Mar 08 2003
STATUS
approved

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Last modified June 1 18:23 EDT 2023. Contains 363076 sequences. (Running on oeis4.)