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)
			(4)
			(5)

(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. http://pi.lacim.uqam.ca/piDATA/fibofact.txt.

Sloane, N. J. A. Sequence A062073 in "The On-Line Encyclopedia of Integer Sequences."