On a functional equation of Ruijsenaars (Q2486933)

The authors offer the general solution, analytic at a point of the real line and having a simple pole at integer multiples of a real number \(p,\) of the functional equation \[ \sum\Bigl[\prod h(x_j-x_i)h(x_i-x_j-ib)-\prod h(x_i-x_j)h(x_j-x_i-kib)\Bigr]=0 \] and from that a proof of a conjecture of \textit{S. N. M. Ruijsenaars} [Commun. Math. Phys. 110, 191--213 (1987; Zbl 0673.58024)]. Here the sum is on all \(k\)-element subsets \(K\) of \(N=\{1,\dots,n\},\) while in the products \(k\) and \(j\) are in \(K\) or \(N\setminus K,\) respectively.