What does “$\prod$” mean?

Question

In the following formula: $$P_i(z)= \prod_{j=0}^{k-1}(z+2^jx_i) \mod 2^k.$$

• What does "$\prod$" mean?

Answer 1

For comparison (if you are familiar with the sigma-notation):

$$\sum_{i=0}^n a_i=a_0+a_1+a_2+\dots+a_n$$ $$\prod_{i=0}^{n}a_i=a_0\times a_1\times a_2\times\dots\times a_n$$

The only difference is that you multiply instead of adding. So $$\boxed{\prod_{j=0}^{k-1}(z+2^jx_i)=(z+2^0x_i)\times (z+2^1x_i)\times(z+2^2x_i)\times\dots\times(z+2^{k-1}x_i)\\=(z+x_i)(z+2x_i)(z+4x_i)\times\dots\times (z+2^{k-1}x_i)}$$

The greek letter $\Sigma$, sigma, is a capital S, and is used to represent sum, similarly the greek letter $\Pi$, pi, is a capital P, and is used to represent product.

Answer 2

The Product of.

So multiply together all the $z + 2^jx_i$ for each $j=0$ to $k-1$.

Answer 3

The symbol you expressed as $$\Pi$$ is known as the product of an expression

in the formula, it says (in words), "P sub i of z = "the product" when j = 0 and goes to k - 1 of z + 2 to the j separated by x sub i where the whole formula is modded by 2 to the k"