|
| |
|
|
A080729
|
|
Decimal expansion of the infinite product of zeta functions for even arguments.
|
|
2
|
|
|
|
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
|
Table of n, a(n) for n=1..105.
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, arXiv:math/0604505.
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
|
Cf. A021002, A080730.
Sequence in context: A098829 A190404 A243433 * A262080 A164800 A011008
Adjacent sequences: A080726 A080727 A080728 * A080730 A080731 A080732
|
|
|
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
|
| |
|
|
