像粒子这样，你需要除以n的阶乘。
现在，让我们回到阶乘函数上来。
这极大地限制了阶乘函数的可能范围。
This limits greatly the possible range of your factorial function.
计算阶乘是递归程序设计的一个经典示例。
The classic example of recursive programming involves computing factorials.
在寄存器3中想要做的是计算此值的阶乘。
What you want to do with this value in register 3 is to calculate the factorial of it.
否则，使用递归函数计算阶乘。
Otherwise, a recursive function is used to calculate the factorial.
写出一个用递归来计算阶乘的函数。
Write a function that calculates a number's factorial using recursion.
编写了阶乘代码后，您可能发现该代码仍有错误。
If you've written factorial code, you've probably noticed that the code is still wrong.
如何使用扩展精度运算处理更大的阶乘？
How to use extended precision arithmetic to handle bigger factorials?
结果稍后将显示在阶乘按钮下方的标签中。
Results will later be displayed in the labels beneath the factorial buttons.
这样将产生一个相对简单的结果，因为阶乘被消去了。
So this is going to turn out to be a relatively simple case, because the factorials are going to cancel.
那让我们在这指出，使用斯特林近似，对每一阶乘项。
So let's just break that out then, and use the Stirling's approximation for each of the factorial terms.
现在符号有两重意义，即组合意义和阶乘意义。
The symbol now has two meanings, the combinatorial and the factorial.
按分解的方法，将一个大数的阶乘用数组实现。
According to the decomposition method, a majority of the factorial using arrays to achieve.
它的功能还包含计算三角函数，阶乘，排列和组合的计算。
Some of the features include trigonometry, factorials, permutations and combinations.
就是说，现在我们要除以NA的阶乘乘以nb的阶乘的积。
That is, now we have to divide by NA factorial times NB factorial.
什么是两阶乘计算任意精度比的一种有效途径？
What would be an efficient way of calculating ratio of two factorials with arbitrary precision?
计算了阶乘之后，现在需要用printf将其打印出来。
After computing the factorial, you now want to print it out using printf.
可以用与Fibonacci序列基本相同的方式对待阶乘。
You can think of factorials in much the same way as Fibonacci sequences.
下面同样是计算阶乘的方法，这次是针对Duby编译器而写的。
The same method to calculate the factorial, this time written for the Duby compiler.
例如，如果我们要计算4的阶乘为多少，到底会发生什么呢？
What happens, for instance, if you try to find the value of the factorial of 4? Let's follow the sequence
计算某个数的阶乘就是用那个数去乘包括1在内的所有比它小的数。
The factorial of a number is computed as that number times all of the Numbers below it up to and including 1.
显然，差分算子及其逆算子是阶乘幂多项式的方便工具。
Clearly, the difference operator or sum operator is the convenient tool for the polynomial of factorial powers.
当计算到零时，没有条件来停止它，所以它会继续调用零和负数的阶乘。
There is nothing to stop it when it hits zero, so it would continue calling factorial on zero and the negative numbers.
发现加入确定性过程将在背景基础上引起明显的阶乘矩行为的变化。
It indicates that behavior of factorial moment will give rise to manifest change when deterministic process is added to other processes.
另一方面，在单事件分析中，使用横向阶乘矩进行计算是有意义的。
On the other hand, the HFNM is in its own right useful in single-event analysis.
首先，设计基于带符号阶乘展开式的椭圆曲线标量乘和多标量乘算法。
Firstly, based on the signed factorial expansions,. The fast algorithms for scalar multiplication and multi-scalar multiplication on elliptic curves are presented.
用蒙特-卡洛模拟方法对纵向阶乘矩和横向阶乘矩进行了比较和研究。
The difference in the horizontal and vertical factorial moments is compared and studied using Monte-Carlo simulation.
在一般情况下，只有在引入累积变量后，纵向阶乘矩才与横向阶乘矩相等。
It is shown that the horizontal and vertical factorial moments are equivalent only when they are used in combination with the cumulant variables.
我们用高速缓存阶乘计算器factorial . py作为类定义的练习，如清单4所示。
For an exercise in class definition, you'll use the caching factorial calculator of factorial.py, shown in Listing 4.
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