# Product of a sequence identities

by eddybob123
Tags: identities, product, sequence
It's an interesting question what would constitute a "non-trivial" product identity. An additive identity $\sum_{i=1}^{\infty} X_i = Y$ implies a product identity $\prod_{i=1}^{\infty} e^{x_i} = e^Y$. A product identity that had negative factors could not be converted back into an additive identity by taking logarithms, but there might be some other methods of transformation that would revert it to an additive identity.