A set of identities involving n-dimensional visible lattice points was discovered by Campbell. Examples include product_((a, b) = 1 a>=0, b<=1) (1 - y^a z^b)^(-1/b) = (1 - z)^(-1/(1 - y)) for left bracketing bar y z right bracketing bar , left bracketing bar z right bracketing bar <1 and product_((a, b, c) = 1 a, b>=0, c<=1) (1 - x^a y^b z^c)^(-1/c) = (1 - z)^(-1/[(1 - x)(1 - y)]) for left bracketing bar x y z right bracketing bar , left bracketing bar x z right bracketing bar , left bracketing bar y z right bracketing bar , left bracketing bar z right bracketing bar <1.