Dyson constant-term identity

For nonnegative integers $a_1,\dots ,a_n$,

When all exponents are positive, the Dyson constant-term identity satisfies $D(a)={\sum }_{i}D(a-e_i)$. This follows from the rational identity ${\sum }_i{\prod }_{j\ne i}(1-X_i/X_j{)}^{-1}=1$, obtained from Lagrange interpolation polynomial at zero. When $a_i=0$, taking the constant term in $X_i$ deletes that coordinate, giving the boundary recurrence.