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Product Formula

Let alpha be a nonzero rational number alpha=+/-p_1^(alpha_1)p_2^(alpha_2)...p_L^(alpha_L), where p_1, ..., p_L are distinct primes, alpha_l in Z and alpha_l!=0. Then

|a|product_(p prime)|alpha|_p=p_1^(alpha_1)p_2^(alpha_2)...p_L^(alpha_L)p_1^(-alpha_1)p_2^(-alpha_2)...p_L^(-alpha_L)
(1)
=1.
(2)

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References

Burger, E. B. and Struppeck, T. "Does sum_(n=0)^(infty)1/(n!) Really Converge? Infinite Series and p-adic Analysis." Amer. Math. Monthly 103, 565-577, 1996.

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Product Formula

Cite this as:

Weisstein, Eric W. "Product Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProductFormula.html

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