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The behavior of () for an increasing positive variable is simple. It grows quickly, faster than an exponential function in fact. Asymptotically as → ∞, the magnitude of the gamma function is given by Stirling's formula

https://en.wikipedia.org/wiki/Gamma_function

where is the golden ratio.It was derived by Binet in 1843, although the result was known to Euler, Daniel Bernoulli, and de Moivre more than a century earlier.

https://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html