A021002 Decimal expansion of zeta(2)*zeta(3)*zeta(4)*...
2, 2, 9, 4, 8, 5, 6, 5, 9, 1, 6, 7, 3, 3, 1, 3, 7, 9, 4, 1, 8, 3, 5, 1, 5, 8, 3, 1, 3, 4, 4, 3, 1, 1, 2, 8, 8, 7, 1, 3, 1, 6, 3, 7, 9, 9, 4, 4, 1, 6, 6, 8, 6, 7, 3, 2, 7, 5, 8, 1, 4, 0, 3, 0, 0, 0, 1, 3, 9, 7, 0, 1, 2, 0, 1, 1, 3, 2, 3, 1, 5, 7, 5, 0, 1, 7, 9, 6, 8, 0, 4, 5, 2, 3, 2, 7, 2, 4, 9, 0, 8, 1, 3, 8, 4
Offset: 1
Examples
2.2948565916733137941835158313443112887131637994416686732758140300...
References
- R. Ayoub, An Introduction to the Analytic Theory of Numbers, Amer. Math. Soc., 1963, p. 198-9.
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274.
Links
- Robert Price, Table of n, a(n) for n = 1..1000
- Steven R. Finch, Abelian Group Enumeration Constants. [From the Wayback machine]
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 86.
- Felix Fontein and Pawel Wocjan, Quantum Algorithm for Computing the Period Lattice of an Infrastructure, arXiv preprint arXiv:1111.1348 [quant-ph], 2011.
- Felix Fontein and Pawel Wocjan, On the probability of generating a lattice, Journal of Symbolic Computation, Vol. 64 (2014), pp. 3-15, arXiv preprint, arXiv:1211.6246 [math.CO], 2012-2013. - From _N. J. A. Sloane_, Jan 03 2013
- 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:0604505 [math.NT], 2006.
- B. R. Srinivasan, On the Number of Abelian Groups of a Given Order, Acta Arithmetica, Vol. 23, No. 2 (1973), pp. 195-205, alternative link.
- Eric Weisstein's World of Mathematics, Abelian Group.
- Index entries for constants related to zeta
Crossrefs
Programs
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Maple
evalf(product(Zeta(n), n=2..infinity), 200);
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Mathematica
p = Product[ N[ Zeta[n], 256], {n, 2, 1000}]; RealDigits[p, 10, 111][[1]] (* Robert G. Wilson v, Nov 22 2005 *) -
PARI
prodinf(n=2,zeta(n)) \\ Charles R Greathouse IV, May 27 2015
Formula
Extensions
More terms from Simon Plouffe, Jan 07 2002
Further terms from Robert G. Wilson v, Nov 22 2005
Mathematica program fixed by Vaclav Kotesovec, Sep 20 2014
Comments