  The normalized characters of Kirillov-Reshetikhin modules over a quantum
affine algebra have a limit as a formal power series. Mukhin and Young found a
conjectural product formula for this limit, which resembles the Weyl
denominator formula. We prove this formula except for some cases in type $E_8$
by employing an algebraic relation among these limits, which is a variant of
$Q\widetilde{Q}$-relations.
