Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions

DOI10.1007/s10440-017-0099-0zbMath1371.41041arXiv1606.07961OpenAlexW3100831025MaRDI QIDQ2402610

Gergő Nemes

Publication date: 20 September 2017

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.07961

zbMATH Keywords

error boundsasymptotic expansionsBessel functionsremainder termsHankel functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Asymptotic representations in the complex plane (30E15)

Related Items (11)

Error bounds for the asymptotic expansion of the Hurwitz zeta function ⋮ Fitting Matérn smoothness parameters using automatic differentiation ⋮ Upper bounds and asymptotic expansion for Macdonald's function and the summability of the Kontorovich-Lebedev integrals ⋮ Inequalities for the modified Bessel function of first kind of non-negative order ⋮ Effective bounds for traces of weak Maass forms ⋮ Globally Exact Asymptotics for Integrals with Arbitrary Order Saddles ⋮ Geodesic projection of the von Mises-Fisher distribution for projection pursuit of directional data ⋮ Large-Parameter Asymptotic Expansions for the Legendre and Allied Functions ⋮ Effective bounds for traces of singular moduli ⋮ An effective bound for the partition function ⋮ Atkinson's formula for the mean square of \(\zeta (s)\) with an explicit error term

Uses Software

• DLMF

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