Fibonorial
Introduction In mathematics, the '''Fibonorial''' , also called the '''Fibonacci factorial''', where  is a nonnegative integer, is defined as the product of the first  positive Fibonacci numbers, i.e. : where  is the th Fibonacci number, and  gives the empty product (defined as the multiplicative identity, i.e. 1).The Fibonorial  is defined analogously to the factorial . The Fibonorial numbers are used in the definition of Fibonomial coefficients (or Fibonacci-binomial coefficients) similarly as the factorial numbers are used in the definition of binomial coefficients.
Asymptotic behaviour The series of fibonorials is asymptotic to a function of the golden ratio : . Here the ''fibonorial constant'' (also called the ''fibonacci factorial constant'')   is defined by , where  and  is the golden ratio.An approximate truncated value of  is 1.226742010720 (see  for more digits).
Almost-Fibonorial numbers Almost-Fibonorial numbers: .Almost-Fibonorial primes: prime numbers among the almost-Fibonorial numbers.
Quasi-Fibonorial numbers Quasi-Fibonorial numbers: .Quasi-Fibonorial primes: prime numbers among the quasi-Fibonorial numbers.
Connection with the q-Factorial The fibonorial can be expressed in terms of the q-factorial and the golden ratio ::
Sequences  Product of first  nonzero Fibonacci numbers . and  for  such that  and  are primes, respectively.
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