On residual transcendental extensions of a valuation with rankv = 2

Let v=v??v? be a valuation of a field K with rankv=2. In this paper a residual transcendental extension w=w??w? of v to K(x) is studied where w? and w? are the residual extensions of v? and v? respectively. A characterization of lifting polynomials is given and the constants w_{(K,v)}(c), ?_{(K,v)}(c), ?_{(K,v)}(c) are defined for c, where (c,?)?K_{v} is the minimal pair defining w.