Rodrigues' descendants of a polynomial and Boutroux curves

Rikard Bøgvad, Christian Hägg, Boris Shapiro

Motivated by the classical Rodrigues' formula, we study the root asymptotic of the polynomial sequence $$R_{[\alpha n],n,P}(z)=\frac{d^{[\alpha n]}{P}^n(z)}{d{z}^{[\alpha n]}},n=0,1,\dots$$ where ${P(…