How do you put conditions on indices in a sum of product?

Question

I would like to know how to interpret the following mathematical expression

$$ \sum_{i=1}^k \prod_{j≠i}^k f(i,j) $$ What puts me in trouble is the “ ≠ ” sign of the product. For example, if i=1, what value does j accept? So, if i=1, j=?, if i=2, j=?, etcetera.

See equation (5) of the paper: “Generalization for the distribution of Hartley's FMAX statistic under heterogeneity of variances with unequal sample sizes”

https://www.researchgate.net/publication/268309165

Thank you very much, Roberto Mioni

Answer 1

$j$ runs from $1$ (this is usually shown as $j=1$ below the big $\Pi$) to $k$ but you skip the term where $j=i$. For each $i$ in the sum you will have $k-1$ terms in the product. If $k=6$ and you are at $i=4$ in the sum, you would have $j$ run through $1,2,3,5,6$.