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Fibonacci Factorial Constant
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
 |  |  |
(3)
|
 |  | ![((-1)^(1/24)phi^(1/12))/(2^(1/3))[theta_1^'(0,-i/phi)]^(1/3)](https://mathworld.wolfram.com/images/equations/FibonacciFactorialConstant/Inline8.svg) |
(4)
|
 |  |  |
(5)
|
(OEIS A062073), where 
is a q-Pochhammer
symbol and 
is a Jacobi
theta function.
See also
Fibonorial, Golden Ratio, Infinite ProductExplore with Wolfram|Alpha
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. https://www.plouffe.fr/simon/constants/fibofact.txt.Sloane, N. J. A. Sequence A062073 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Fibonacci Factorial ConstantCite this as:
Weisstein, Eric W. "Fibonacci Factorial Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FibonacciFactorialConstant.html