Sharp error bounds for turning point expansions

2020/09/10 by Dunster, T. M., Gil, A., Segura, J.
#33C10 #34E05 #34E20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.04666

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.

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