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

We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral, ${\int }_{0}^{\mathrm{\infty }}\mathrm{f}\left(\mathrm{x}\right)$ Jν(bx) dx as b → ∞, using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function,...

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Veröffentlicht in:	Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2014-02, Vol.470 (2162), p.1-16
Hauptverfasser:	Galapon, Eric A., Martinez, Kay Marie L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Asymptotic series Asymptotic value Bessel functions Gamma function Integers Mathematical integrals Series convergence Series expansion
Online-Zugang:	Volltext
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