question about maths notation

I am well familiar with the conventional sum notation such as if you want to express:

x{1} + x{1}^2
+ x{2} + x{2}^2
+ x{3} + x{3}^2
...
+ x{n} + x{n}^2

( let {.} be for subscript here )

you simply write that down in conventional shorthand as:

∑[x=1, n] x + x^2

But is there a similar shorthand standard conventional way for when you wanted to express not the sum but a product such as:

(x{1} + x{1}^2 )
* ( x{2} + x{2}^2 )
* ( x{3} + x{3}^2 )
...
* ( x{n} + x{n}^2 )

?

I was thinking about keeping it very simple in my book and write that down simply as:

product[x=1, n] x + x^2

but I want to first check there isn't a standard conventional way of expressing that which differs from that; better I think to stick to convention unless you have or can find a specific reason not to.

Here you go:
https://en.wikipedia.org/wiki/Infinite_product

It uses a Pi

Sums of a sequence are called series. I can find no equivalent name for products of a sequence. The Wikipedia articles I have checked so far just call them products.

Originally posted by twhitehead
Here you go:
https://en.wikipedia.org/wiki/Infinite_product

It uses a Pi

Sums of a sequence are called series. I can find no equivalent name for products of a sequence. The Wikipedia articles I have checked so far just call them products.

Arr thanks.
Now I know what to search for, I found this:
https://en.wikipedia.org/wiki/Product_%28mathematics%29
"...Product of sequences:
The product operator for the product of a sequence is denoted by the capital Greek letter Pi ∏ (in analogy to the use of the capital Sigma ∑ as summation symbol). The product of a sequence consisting of only one number is just that number itself. The product of no factors at all is known as the empty product, and is equal to 1.
..."

So that is obviously what I should (and will ) use in my book.

Originally posted by humy
Arr thanks.
Now I know what to search for, I found this:
https://en.wikipedia.org/wiki/Product_%28mathematics%29
"...Product of sequences:
The product operator for the product of a sequence is denoted by the capital Greek letter Pi ∏ (in analogy to the use of the capital Sigma ∑ as summation symbol). The product of a sequence consisting of only one number i ...[text shortened]... duct, and is equal to 1.
..."

So that is obviously what I should (and will ) use in my book.

We will want a copy🙂

Originally posted by sonhouse
We will want a copy🙂

seriously, I think I will give a few free copies on personal requests (after asking if anyone wants one ) to people here when finally I have finished it (no where near finished yet! ) and it is published.
I am hoping it will be finished and published some time before the end of this year.
My book will revolutionize the world of philosophy and have a powerful influence (wouldn't go as far as say 'revolutionize' ) on the world of statistics and also I think should revolutionize artificial intelligence.

Originally posted by humy
seriously, I think I will give a few free copies on personal requests (after asking if anyone wants one ) to people here when finally I have finished it (no where near finished yet! ) and it is published.
I am hoping it will be finished and published some time before the end of this year.
My book will revolutionize the world of philosophy and have a po ...[text shortened]... on the world of statistics and also I think should revolutionize artificial intelligence.

Is this going to be your Phd thesis? Is this going to somehow quantize philosophy? Can't wait!