The Fibonacci factorial constant is the constant appearing in the asymptotic growth of the fibonorials (aka. Fibonacci factorials) .
It is given by the infinite product
(1)
where
(2)
and
is the golden ratio .
It can be given in closed form by
(OEIS A062073 ), where is a q -Pochhammer
symbol and is a Jacobi
theta function .
See also Fibonorial ,
Golden
Ratio ,
Infinite Product
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References Finch, S. R. "Fibonacci Factorials." §1.2.5 in Mathematical
Constants. Cambridge, England: Cambridge University Press, p. 10, 2003. Graham,
R. L.; Knuth, D. E.; and Patashnik, O. Concrete
Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley,
pp. 478 and 571, 1994. Plouffe, S. http://pi.lacim.uqam.ca/piDATA/fibofact.txt . Sloane,
N. J. A. Sequence A062073 in "The
On-Line Encyclopedia of Integer Sequences." Referenced on Wolfram|Alpha Fibonacci Factorial Constant
Cite this as:
Weisstein, Eric W. "Fibonacci Factorial Constant."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/FibonacciFactorialConstant.html
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