Let x be a complex number.


What is the Stirling formula for x(x+1)(x+2)...(x+n-1) when n goes to infinity?



What is the Stirling formula for x(x+1)(x+2)...(x+n-1)?
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](http://functions.wolfram.com/GammaBetaErf/Pochhammer/introductions/FactorialBinomials/ShowAll.html):


$$(x)\_n \sim \frac{2\pi}{\Gamma(x)} e^{-n}n^{x+n-\frac12}(1+O(\frac1n)) \qquad n \to \infty$$


