Exactification of the method of steepest descents: the Bessel functions of large order and argument

DOI10.1098/RSPA.2004.1307zbMath1071.65024OpenAlexW2082814086MaRDI QIDQ3024580

Richard B. Paris

Publication date: 1 July 2005

Published in: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2004.1307

zbMATH Keywords

asymptoticsnumerical examplesBessel functionsconfluent hypergeometric functionsmethod of steepest descentshyperasymptoticsHadamard expansionsLaplace-type integrals

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Numerical approximation and evaluation of special functions (33F05)

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Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions ⋮ On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. IV: Poles ⋮ On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. III: Clusters of saddle points ⋮ Superinterpolation in highly oscillatory quadrature ⋮ The evaluation of Bessel functions via exp-arc integrals ⋮ The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions ⋮ High-precision evaluation of the Bessel functions via Hadamard series ⋮ Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales ⋮ Hadamard expansions for integrals with saddles coalescing with an endpoint

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