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Fibonacci Factorial Constant
The Fibonacci factorial constant is the constant appearing in the asymptotic growth of thefibonorials (aka. Fibonacci factorials)
. It is given by theinfinite product
 | (1) |
where
 | (2) |
and
is thegolden 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)](/image.pl?url=http%3a%2f%2fmathworld.wolfram.com%2fimages%2fequations%2fFibonacciFactorialConstant%2fInline8.svg&f=jpg&w=240) | (4) |
 |  |  | (5) |
(OEISA062073), where
is aq-Pochhammer symbol and
is aJacobi theta function.
See also
Fibonorial,GoldenRatio,Infinite ProductExplore with Wolfram|Alpha
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References
Finch, S. R. "Fibonacci Factorials." §1.2.5 inMathematical 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. SequenceA062073 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Fibonacci Factorial ConstantCite this as:
Weisstein, Eric W. "Fibonacci Factorial Constant."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/FibonacciFactorialConstant.html