A242623 Decimal expansion of Product_{n>1} (1+1/n)^(1/n).

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

Offset: 1

Author

Jean-François Alcover, May 19 2014

Keywords

• nonn
• cons

Examples

			1.758743627951184824699896849661932...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 p. 122.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A131688, A242624, A244625.

Programs

Magma

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

Maple

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

Mathematica

Exp[NSum[((-1)^n*(-1 + Zeta[n]))/(n - 1), {n, 2, Infinity}, NSumTerms -> 300, WorkingPrecision -> 105] ] // RealDigits[#, 10, 103]& // First (* edited by Jean-François Alcover, May 23 2014 *)

PARI

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

SageMath

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

Formula

Equals exp(A131688)/2.

Extensions

Data extended by Jean-François Alcover, May 23 2014