Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales

DOI10.1098/RSPA.2013.0529zbMath1348.33004OpenAlexW2105833598WikidataQ51114079 ScholiaQ51114079MaRDI QIDQ2831318

Kay Marie L. Martinez, Eric A. Galapon

Publication date: 2 November 2016

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

Full work available at URL: https://doi.org/10.1098/rspa.2013.0529

zbMATH Keywords

asymptoticsdistributional approachHankel integral

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (3)

Exact expansions of Hankel transforms and related integrals ⋮ Regularized limit, analytic continuation and finite-part integration ⋮ Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. I. Integer orders

Cites Work

• Numerical evaluation of functions arising from transformations of formal series
• The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
• Exactification of the asymptotics for Bessel and Hankel functions.
• Asymptotic expansion of a class of integral transforms via Mellin transforms
• Exactification of the method of steepest descents: the Bessel functions of large order and argument
• Hyperasymptotics
• A procedure for summing asymptotic series
• Asymptotic Expansion of Laplace Transforms Near the Origin

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