Polynomials biorthogonal to dilations of measures, and their asymptotics

We analyze polynomials Pn that are biorthogonal to dilates of a positive measure μ, supported on (0,∞): ∫0∞Pn(x)dμ(σn,jx)=0,1≤j≤n. We establish representations for Pn in terms of the associated dilation polynomialRn(y)=∏j=1n(y+1/σn,j). In the case where dμ(t)=tαe−tβdton (0,∞), we show that strong asymptotics for Rn in the complex plane, as n→∞, lead to strong asymptotics for Pn, via the method of steepest descent.