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A080729 Decimal expansion of the infinite product of zeta functions for even arguments. 5
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.
Bernd C. Kellner, On asymptotic constants related to products of Bernoulli numbers and factorials, Integers, Vol. 9 (2009), Article #A08, pp. 83-106; alternative link; arXiv preprint, arXiv:math/0604505 [math.NT], 2006-2009.
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 (A000688), then Product_{k>=1} zeta(2*k) = Sum_{k>=1} u(k)/k^2. - Benoit Cloitre, Jun 25 2003
Equals A021002/A080730. - Amiram Eldar, Jan 31 2024
EXAMPLE
1.82101745149929239040672513222600684857...
MATHEMATICA
RealDigits[Product[Zeta[2n], {n, 500}], 10, 110][[1]] (* Harvey P. Dale, Jan 31 2012 *)
PROG
(PARI) prodinf(k=1, zeta(2*k)) \\ Vaclav Kotesovec, Jan 29 2024
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 March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)