List of Representations of E - As An Infinite Product

As An Infinite Product

The number e is also given by several infinite product forms including Pippenger's product

and Guillera's product

$e = \left ( \frac{2}{1} \right )^{1/1} \left (\frac{2^2}{1 \cdot 3} \right )^{1/2} \left (\frac{2^3 \cdot 4}{1 \cdot 3^3} \right )^{1/3} \left (\frac{2^4 \cdot 4^4}{1 \cdot 3^6 \cdot 5} \right )^{1/4} \cdots ,$

where the nth factor is the nth root of the product

as well as the infinite product

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