Tagged Questions
5
votes
1answer
100 views
Generalization of the Factorial function
Is there any standard generalization of the Factorial function where the "skips" per multiplication is a parameter? For example, one generalization could be: $a(a-b)(a-2b)(a-3b)...1$
I tried to ...
6
votes
1answer
229 views
Ramanujan's approximation to factorial
I saw this approximation for the factorial given by Ramanujan as
$$\log(n!) \approx n \log n - n + \frac{\log(n(1+4n(1+2n)))}{6} + \frac{\log(\pi)}{2}$$ in wikipedia, which claims the approximation is ...
13
votes
2answers
327 views
On the Limit of Stirling's Approximation
I have recently proven the following curious identity: For real $x \geqslant 1$,
\begin{align}
\lfloor x \rfloor! = x^{\lfloor x \rfloor} e^{1-x} e^{\int_{1}^{x} \text{frac}(t)/t \ dt}
\end{align}
...
