Let x be a complex number.
What is the Stirling formula for x(x+1)(x+2)...(x+n1) when n goes to infinity?
Let x be a complex number. What is the Stirling formula for x(x+1)(x+2)...(x+n1) when n goes to infinity? 


It looks like you want a formula for the asymptotics of the Pochhammer symbol $(x)_n$ as $n \to \infty$. One such formula is provided about halfway down Wolfram's page: $$(x)_n \sim \frac{2\pi}{\Gamma(x)} e^{n}n^{x+n\frac12}(1+O(\frac1n)) \qquad n \to \infty$$ 

