A175619 Decimal expansion of Product_{n>=2} (1-n^(-8)).
9, 9, 5, 9, 2, 3, 3, 1, 5, 0, 7, 7, 7, 8, 3, 6, 7, 1, 2, 0, 4, 1, 0, 6, 7, 4, 7, 3, 0, 8, 6, 0, 6, 6, 6, 7, 0, 6, 6, 2, 3, 0, 0, 1, 7, 2, 9, 6, 3, 3, 6, 3, 7, 2, 3, 9, 9, 8, 3, 3, 6, 3, 3, 0, 0, 2, 6, 0, 0, 0, 3, 1, 6, 8, 3, 0, 3, 1, 1, 9, 4, 0, 8, 9, 6, 9, 0, 7, 2, 9, 7, 6, 1, 2, 9, 0, 8, 5, 3, 2, 6, 4, 4, 0, 7
Offset: 0
Examples
0.9959233150... = (255/256)*(6560/6561)*(65535/65536)*...
Links
- E. Weisstein, Infinite Product, Mathworld.
Programs
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Maple
t := Pi/sqrt(2) ; sinh(Pi)*((sin(t)*cosh(t))^2+(cos(t)*sinh(t))^2)/8/Pi^3 ; evalf(%) ;
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Mathematica
RealDigits[ -Sin[(-1)^(1/4)*Pi]*Sin[(-1)^(3/4)*Pi]*Sinh[Pi] / (8*Pi^3) // Re, 10, 105] // First(* Jean-François Alcover, Feb 12 2013 *)
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PARI
exp(suminf(j=1, (1 - zeta(8*j))/j)) \\ Vaclav Kotesovec, Apr 27 2020
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PARI
prodnumrat(1-x^-8, 2) \\ Charles R Greathouse IV, Feb 04 2025
Formula
Equals (cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi)) * sinh(Pi) / (16*Pi^3). - Vaclav Kotesovec, Apr 27 2020
Equals exp(Sum_{j>=1} (1 - zeta(8*j))/j). - Vaclav Kotesovec, Apr 27 2020