How to calculate summation Σ and product Π

・In Japanese

■summation:Σ

Σ represents the summation.The following calculates the sum of a sequence of numbers.



The number below Σ means k starts with 1, and the letter above Σ means k ends with n. For example, it could look like this:



＜Specific example (1):mean value＞
The mean value can be expressed as follows.



＜Specific example (2):sum of arithmetic progressions＞
The sum of an arithmetic progression can be expressed as follows.



＜Specific example (3)-1:double Σ＞
When using two sigmas, calculations are performed starting from the inner sigma.



This is easier to understand if you imagine the sum of each term in the two-dimensional map below.



＜Specific example (3)-2:double Σ＞
In the following cases, calculate by dividing Σ.

■product:π

π stands for product, and the following cases calculate the product of sequences.



An example of the use of π is in the transfer function of a Butterworth filter.

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