A115522 Decimal expansion of (Glaisher^12/(2*Pi*e^EulerGamma))^(Pi^2/6).

2, 5, 5, 3, 7, 1, 2, 6, 8, 2, 7, 4, 8, 2, 0, 9, 0, 5, 2, 9, 3, 9, 3, 1, 4, 5, 7, 4, 4, 4, 0, 9, 6, 4, 0, 7, 8, 6, 6, 7, 1, 5, 1, 0, 3, 8, 2, 1, 4, 8, 1, 7, 1, 2, 8, 1, 3, 5, 3, 6, 0, 1, 3, 4, 5, 9, 6, 6, 9, 8, 2, 5, 8, 4, 5, 6, 9, 0, 6, 2, 7, 7, 1, 0, 6, 1, 1, 7, 3, 7, 6, 5, 3, 5, 4, 4, 3, 6, 7, 5, 3, 4, 5, 3, 8

Offset: 0

Author

Eric W. Weisstein, Jan 25 2006

Keywords

• nonn
• cons

Examples

			2.5537126827482090529...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.

Links

• Robert A. Van Gorder, Glaisher-type products over the primes, International Journal of Number Theory, Vol. 8, No. 2 (2012), pp. 543-550.
• Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant.

Crossrefs

Cf. A000796, A001113, A001620, A073002, A074962.

Programs

Mathematica

RealDigits[(Glaisher^12/(2Pi E^EulerGamma))^(Pi^2/6),10,100][[1]] (* Vaclav Kotesovec, Aug 15 2015 after Eric W. Weisstein *)

Formula

Equals Product_{k>=1} k^(1/k^2). - Vaclav Kotesovec, Dec 10 2017

Equals (Product_{k>=1} prime(k)^(1/(prime(k)^2-1)))^(Pi^2/6) (Van Gorder, 2012). - Amiram Eldar, Jul 22 2022

Equals exp(-zeta'(2)). - Vaclav Kotesovec, Jun 22 2023