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%I #12 Jul 03 2022 18:06:05
%S 6,0,3,4,9,6,4,4,1,8,2,2,3,1,3,4,8,3,4,7,0,1,1,0,0,6,8,0,5,1,7,0,2,7,
%T 1,8,9,6,0,2,3,0,9,6,3,6,4,9,4,7,8,4,3,6,0,9,6,4,4,0,4,2,0,2,1,5,4,4,
%U 8,7,4,0,2,9,0,7,4,7,0,1,0,1,3,3,7,0,2
%N Decimal expansion of the geometric integral of the Riemann zeta function from 1 to infinity.
%C The geometric integral of a function, f(x), from a to b is defined as lim_{dx->0} Product_{i=1..n} f(x_i)^dx, where n = (b - a)/dx and x_i is a number on the interval [a + dx*(i-1), a + dx*i].
%C The geometric integral can be shown to be equivalent to exp(Integral_{a..b} log(f(x)) dx).
%H Iain Fox, <a href="/A355251/b355251.txt">Table of n, a(n) for n = 1..2000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Product_integral">Product integral</a>
%F Equals exp(Integral_{s=1..oo} log(zeta(s)) ds) = e^A188157.
%e Equals 6.03496441822313483470110068051702718960230963649478436096...
%o (PARI) exp(intnum(s=1, [oo, log(2)], log(zeta(s))))
%Y Cf. A001113, A188157.
%K nonn,cons
%O 1,1
%A _Iain Fox_, Jun 26 2022
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