FROM CONTINUOUS PAINLEVE-IV TO THE ASYMMETRIC DISCRETE PAINLEVE-I

We examine the discrete equation that is obtained from the Schlesinger transformations of the continuous Painleve IV equation. The use of th e Schlesinger transformations naturally establishes the Lax pair of th e discrete equation which is an asymmetric form of d-P-I and has P-II as continuous limit. We analyse the transformations of the discrete eq uation and show that they lead to a self-dual description where the di screte equation and the Schlesinger's play the same role. Finally, usi ng the relation between P-IV and asymmetric d-P-I we examine in detail the special solutions of both equations.