What,s the meaning of this expression?

1. Apr 15, 2006

eljose

Let be the expression:

$$\Product_{p}(1+x^{p})$$ where the product is extended to over all primes.

of course is some kind of generalizating the function $$\Product_{m=1}^{\infty}(1+x^{m})$$ wich is some partition function..but what happens when is evaluated only in primes?..thanks.

2. Apr 15, 2006

matt grime

It's \Prod, not \Product.

It is some partition in to some sets of cardinality a certain kind (square free will have some bearing on it, by the looks of it).

3. Apr 15, 2006

eljose

O sorry then $$\Prod_{p}(1+x^{p})$$ i think i saw it as an example inside the Tom Apostol,s book "Introduction to Analytic number theory"..in the part refering to "Partition function"...

4. Apr 15, 2006

matt grime

Or perhaps \prod, even, and not \Prod.

$$\prod, \Prod$$