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What,s the meaning of this expression?

  1. Apr 15, 2006 #1
    Let be the expression:

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

    of course is some kind of generalizating the function [tex] \Product_{m=1}^{\infty}(1+x^{m}) [/tex] wich is some partition function..but what happens when is evaluated only in primes?..thanks.
     
  2. jcsd
  3. Apr 15, 2006 #2

    matt grime

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    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).
     
  4. Apr 15, 2006 #3
    O sorry then [tex] \Prod_{p}(1+x^{p}) [/tex] 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"...
     
  5. Apr 15, 2006 #4

    matt grime

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

    [tex]\prod, \Prod[/tex]
     
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