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 <sup>th</sup> 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.
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 primes: prime numbers among the almost-Fibonorial numbers.
Quasi-Fibonorial numbers: .
Quasi-Fibonorial primes: prime numbers among the quasi-Fibonorial numbers.
The fibonorial can be expressed in terms of the q-factorial and the golden ratio :
Product of first nonzero Fibonacci numbers .
and for such that and are primes, respectively.