Question

Approximating factorial using identity $\frac{1}{x}!\frac{2}{x}!\cdots\cdot\frac{x}{x}!=\frac{ {x}!\cdot(2\pi)^{\frac{x-1}{2}} }{ x^x\cdot\sqrt{x} }$

score 150 · Answer 1 · 2026-04-17 15:48:17

150

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Approximating factorial using identity $\frac{1}{x}!\frac{2}{x}!\cdots\cdot\frac{x}{x}!=\frac{ {x}!\cdot(2\pi)^{\frac{x-1}{2}} }{ x^x\cdot\sqrt{x} }$

Published on 17 Apr 2026 - 15:48

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67

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98

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235

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List Question

Approximating factorial using identity $\frac{1}{x}!\frac{2}{x}!\cdots\cdot\frac{x}{x}!=\frac{ {x}!\cdot(2\pi)^{\frac{x-1}{2}} }{ x^x\cdot\sqrt{x} }$

Approximating Functions: Taylor Approximation vs. Fourier Approximation

What are some alternatives to least squares method?

Find an approximation for the number of times you have to find a random variable

How to simplify this big-O notation?

Any approximation for $1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots + \frac{x^n}{n!}$ for finite $n$?

How to find the approximate error in Stirlings Formula

Is it just coincidence that $e + 2\pi$ is very close to 9?

Is the fact that $\int_{0}^{\infty} \cos(2x)\prod_{n=1}^{\infty} \cos\big(\frac{x}{n}\big) dx\approx \frac{\pi}{8}$ a pure numerical coincidence?

Distribution of the argmax of a Gaussian of diagonal variance

Approximating tanh by a rational function

Approximately solving nonlinear trigonometric system

Efficiently approximating the integral of $\operatorname{erf}(x y) \exp(-x^2)$

Approximations of $\sum_{n=0}^\infty\frac{x^n}{n!}$ and $\sum_{n=0}^\infty\frac{x^n}{n!^2}$

Inequality of Lp-norm with supremum

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