Painlevé IV, Chazy II, and asymptotics for recurrence coefficients of semi‐classical Laguerre polynomials and their Hankel determinants

This paper studies the monic semi-classical Laguerre polynomials based on previous work by Boelen and Van Assche, Filipuk et al., Clarkson Jordaan. al. proved that diagonal recurrence coefficient α n ( t ) $$ {\alpha}_n(t) satisfies fourth Painlevé equation. In this paper, we show off-diagonal β {\beta}_n(t) fulfills first member of Chazy II system. We also prove sub-leading both continuous discrete Jimbo–Miwa–Okamoto σ \sigma -form IV. By using Dyson's Coulomb fluid approach together with system for , obtain large asymptotic expansions coefficients coefficient. The asymptotics associated Hankel determinant (including constant term) is derived from its integral representation in terms