A244625 Decimal expansion of Product_{n>1} (1 - 1/n^2)^(1/n).

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

Offset: 0

Author

Jean-François Alcover, Jul 02 2014

Keywords

• nonn
• cons

Examples

			0.7993704013063328789872528539753525668777...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 Alladi-Grinstead Constant, p. 122.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A085361, A242623, A242624.

Programs

Magma

SetDefaultRealField(RealField(100)); L:=RiemannZeta();  Exp(-(&+[(Evaluate(L, 2*n+1)-1)/n: n in [1..10^3]])); // G. C. Greubel, Nov 15 2018

Maple

evalf(exp(-sum((Zeta(2*n+1)-1)/n, n=1..infinity)), 120); # Vaclav Kotesovec, Dec 11 2015

Mathematica

digits = 102; Exp[-NSum[(Zeta[2*n+1]-1)/n, {n, 1, Infinity}, NSumTerms -> 300, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First

PARI

default(realprecision, 100); exp(-suminf(n=1, (zeta(2*n+1)-1)/n)) \\ G. C. Greubel, Nov 15 2018

Sage

numerical_approx(exp(-sum((zeta(2*n+1)-1)/n for n in [1..1000])), digits=100) # G. C. Greubel, Nov 15 2018

Formula

Equals exp(-Sum_{n>0} (zeta(2*n+1) - 1)/n).

Equals A242623 * A242624.

Also equals A242623 * exp(-A085361).