# Author's software

#### Being tested

Multiple factorial

Writing functions:

factorialmulti(a, b)

The function definition :

Multiple factorial function: if the value of b=1, the feature is a factorial, when b=2 - double factorial b. Determines the step by which to change the difference between elements, for example:

factorialmulti(17, 3)=17*14*11*8*5*2

factorialmulti(23, 5)=23*18*13*8*3

We use mathematical functions every day, without even thinking about how they work. However, there are functions that go beyond the usual understanding. One of these functions is a multiple factorial.

A multiple factorial is a function that uses the concept of a factorial and performs it not once, but several times. This function is indicated by a double exclamation mark following the number. For example, 5!! means a multiple factorial of the number 5. Note that at the very beginning we calculate the factorial of the number, and then apply it to the result.

Why do we need such a feature and where can we apply it? The answer is very simple - in mathematics and statistics. The multiple factorial is widely used to calculate various combinatorial problems. For example, when calculating the number of ways to rearrange elements in a sequence or when calculating the number of possible outcomes in random events. The multiple factorial also finds application in probability theory and combinatorics, where it is required to calculate various combinations of elements or subsets.

Now that we know what a multiple factorial is and its application, let's look at how it can be used in practice. Suppose we have a task to calculate the number of combinations. In this case, we can apply a multiple factorial to get an accurate result.

For example, we need to calculate the number of paths that can be taken from one point to another, moving only along the lines along which the points are present. To do this, we can use the combination formula to calculate the number of possible routes. And this is where the multiple factorial comes to our rescue.

So, we know that the multiple factorial is executed several times, and this is its feature. If we want to calculate how many ways there are to go from one point to another, moving only along the lines, then we can use a multiple factorial. For example, to calculate the number of ways to go from point A to point B, we apply a double factorial to the difference between the values of the x and y coordinates.

Thus, the multiple factorial is a convenient and powerful mathematical function that finds application in combinatorics, probability theory and other fields. Its use helps us solve complex problems related to the number of possible combinations and outcomes. Therefore, understanding and the ability to apply multiple factorial in practical problems can become a valuable tool for professional mathematicians and statisticians.