Is this an empty product? Assume that we have: $$\Psi_{j,k}=(t_{j+1}-\tau)\times...\times(t_{j+k-1}-\tau)$$ that can be written as: $$\Pi_{i=j+1}^{j+k-1} (t_i-\tau)$$ If we have $k=1$ , my text-book says that this is an empty product and equals $1$ by definition. It seems to make sense because in this case the "upper limit" of the product is lower than the lower one, but following the first expression, couldn't we write $$\Psi_{j,1}=(t_{j+1}-\tau)\times(t_{j}-\tau)$$ Is this wrong? I am not familiar with this notation and it may be very trivial.

Read : $\Pi_{i=j+1}^{j+k-1} (t_i-\tau)$ as

" _The product of $t_i - \tau$ **FROM** $j+1$ **TO** $j+k-1$_"

Now if $j+1$ is less than $j+k-1$, than the previous assertion makes no sense and by convention we replace the product by $1$.