Sharp error bounds for turning point expansions

ABSTRACT: Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the bounds is illustrated numerically with an application to Bessel functions of large order.Financial support from Ministerio de Ciencia e Innovación Spain, project PGC2018-098279-B-I00 (MCIU/AEI/FEDER, UE) is acknowledged