Hyperasymptotic solutions of second-order linear differential equations. I

DOI10.4310/MAA.1995.v2.n2.a4zbMath0847.34060MaRDI QIDQ1907525

Yanyan Li

Publication date: 8 October 1996

Published in: Methods and Applications of Analysis (Search for Journal in Brave)

zbMATH Keywords

holomorphiclinear differential equations of the second orderPoincaré asymptotic expansionsseries of generalized exponential integralssuperasymptotic expansions

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Ordinary differential equations in the complex domain (34M99) Asymptotic expansions of solutions to ordinary differential equations (34E05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

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The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics ⋮ Exact and approximate energy sums in potential wells ⋮ On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals. I: Real variable ⋮ Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions ⋮ On the numerical solution of second order ordinary differential equations in the high-frequency regime ⋮ Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles ⋮ Numerical methods for the computation of the confluent and Gauss hypergeometric functions ⋮ High-precision computation of the confluent hypergeometric functions via Franklin-Friedman expansion ⋮ Hyperdeterminants. I ⋮ Hyperasymptotics and hyperterminants: exceptional cases ⋮ High-precision evaluation of the Bessel functions via Hadamard series ⋮ Exactification of the asymptotics for Bessel and Hankel functions. ⋮ Improved estimates for nonoscillatory phase functions

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