A080729 Decimal expansion of the infinite product of zeta functions for even arguments.

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

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