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A355251 Decimal expansion of the geometric integral of the Riemann zeta function from 1 to infinity. 1
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, 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, 8, 7, 4, 0, 2, 9, 0, 7, 4, 7, 0, 1, 0, 1, 3, 3, 7, 0, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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].
The geometric integral can be shown to be equivalent to exp(Integral_{a..b} log(f(x)) dx).
LINKS
Wikipedia, Product integral
FORMULA
Equals exp(Integral_{s=1..oo} log(zeta(s)) ds) = e^A188157.
EXAMPLE
Equals 6.03496441822313483470110068051702718960230963649478436096...
PROG
(PARI) exp(intnum(s=1, [oo, log(2)], log(zeta(s))))
CROSSREFS
Sequence in context: A087014 A176906 A293255 * A094174 A105873 A011380
KEYWORD
nonn,cons
AUTHOR
Iain Fox, Jun 26 2022
STATUS
approved

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Last modified June 21 21:50 EDT 2024. Contains 373559 sequences. (Running on oeis4.)