Fibonacci Factorial Constant
المؤلف:
Finch, S. R.
المصدر:
"Fibonacci Factorials." §1.2.5 in Mathematical Constants. Cambridge, England: Cambridge University Press
الجزء والصفحة:
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5-12-2020
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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
(OEIS A062073), where 
is a q-Pochhammer symbol and 
is a Jacobi theta function.
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://pi.lacim.uqam.ca/piDATA/fibofact.txt.
Sloane, N. J. A. Sequence A062073 in "The On-Line Encyclopedia of Integer Sequences."
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