Can anyone tell me about taking products of two capital pi's, One capital pi followed by the other?

Answer 1

See: http://en.wikipedia.org/wiki/Infinite_product

Each represents one part of an infinite product.

For example, if we have a set of numbers a(i,j), with two subscripts i,j between 1 and n, then this product:

http://cheeser1.slyip.com/interspace/prod.gif

represents the product of all possible a(i,j). With two subscripts, you'd want two products. By the way, this double-product is the determinant of an n x n matrix.

Another example: http://cheeser1.slyip.com/interspace/prod2.gif

Notice here that you don't need subscripts. This is simply a product defined over all primes p and all primes q. The product works out to be 0, of course.

Answer 2

Similar to taking the sum of a set of numbers, the "capital pi notation" takes the multiplication of a set of numbers.

"PI" (1+1/x) from x = 2 to 4 is (1+1/2)*(1+1/3)*(1+1/4)

So now lets say you have:
"PI""PI" (1-1/y)*(1+1/x) where the first PI is y from 7 to 8 and the second PI is x from 2 to 4, you execute the x (inner) PI first....

"PI"(1-1/y)(1+1/2)(1+1/3)(1+1/4)

now execute the other "PI":

(1-1/7)(1+1/2)(1+1/3)(1+1/4) * (1-1/8)(1+1/2)(1+1/3)(1+1/4)

it is hard to explain without using the actual notation, but I hope this helps!

Answer 3

Since Pi is undefined, its square (product of a Pi multilied by Pi) will also be undefined but for most of the practical purposes, we can 3.1416 as the value of pi and hence

3.1416 x 3.1416 = 9.86965...= 9.8697 for most of practical purposes.

Answer 4

i have never heard of capital pi's.

anyways, u multiply 3.14 times 3.14 to get a product of pis.

3.14 * 3.14 = 9.8596

Answer 5

n
Πf(i) = f(1)*f(2)*f(3)*f(4)* . . . f(n)
i=1
times
n
Πg(i) = g(1)*g(2)*g(3)*g(4)* . . . g(n)
i=1
equals

f(1)*f(2)*f(3)*f(4)* . . f(n)g(1)*g(2)*g(3)*g(4)* . . g(n)
equals
n
Πf(i)g(i)
i=1