What,s the meaning of this expression?

[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 $$\Product_{m=1}^{\infty}(1+x^{m})$$ which is some partition function..but what happens when is evaluated only in primes?..thanks.

 

[matt grime]

It's \Prod, not \Product.It is some partition into some sets of cardinality a certain kind (square free will have some bearing on it, by the looks of it).

 

[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 referring to "Partition function"...

 

[matt grime]

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

$$\prod, \Prod$$