High-order derivatives of the Bessel functions with an application

2019/05/12 by Paris, R B
#33C10 #34E05 #41A30 #41A60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.04673

Abstract

We determine the asymptotic behaviour of the nth derivatives of the Bessel functions J_ν(a) and K_ν(a), where a is a fixed positive quantity, as n→∞. These results are applied to the asymptotic evaluation of two incomplete Laplace transforms of these Bessel functions on the interval [0,a] as the transform variable x→+∞. Similar evaluation of the integrals involving the Bessel functions Y_ν(t) and I_ν(t) is briefly mentioned.

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