A generalisation of the Stieltjes relations for the Painleve-IV transcendents and
their higher analogues determined by the dressing chains is proposed. It is proven that
if a rational function from a certain class satisfies these relations it must be a solution
of some higher Painleve-IV equation. The approach is based on the interpretation of
the Stieltjes relations as local trivial monodromy conditions for certain Schrodinger
equations in the complex domain. As a corollary a new class of the Schrodinger operators
with trivial monodromy is constructed in terms of the Painleve-IV transcendents.
This is a pre-print. The definitive version: VESELOV, A.P.,2001. On Stieltjes relations, Painleve-IV hierarchy and complex monodromy. Journal of Physics A - Mathematical and General, 34(16), pp.3511-3519, is available at: http://www.iop.org/EJ/journal/JPhysA.