How do I interpret Pi Product notation with no boundaries?

39 Views Asked by At

I came across the following formula in this paper and am struggling with how to interpret it.

$$P_{Z,SWII}(z) = \sum_{i=1}^N \frac{a_i^{N-2}e^{(\frac{-z}{a_i})}}{\prod_{k\neq i}(a_i - a_k)}$$

In particular, over what values do I evaluate the product in the denominator? Is it everything from $k=1$ to $k=N$ excluding $k=i$? Or just $k=1$ to $k=i-1$? Or something else entirely?

I'm particularly confused because though the author derived this formula supposing that values of $a_i$ are "strictly different", in my application they may be equal.