Infinite product

  • Thread starter AntonioM
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when does infinite product have a value not equal to zero or one?
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Char. Limit

Gold Member
I assume you mean a convergent infinite product, because a divergent infinite product has the simple example

[tex]\prod^{\infty}_{i=2} \left(1 + \frac{1}{i}\right)[/tex]

For a convergent infinite product, I offer up this example:

[tex]\prod^{\infty}_{i=1} \left(\frac{1}{1-\left(\frac{1}{p_i}\right)^2}\right) = \frac{\pi^2}{6}[/tex]

That is, incidentally, the Euler Product.

EDIT: Forgot to mention, [itex]p_i[/itex] means the ith prime number.

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