Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions
In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found and used to obtain sharp and realistic error bounds. We also...
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| Veröffentlicht in: | Acta applicandae mathematicae 2017-08, Vol.150 (1), p.141-177 |
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| description | In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found and used to obtain sharp and realistic error bounds. We also give re-expansions for these remainder terms and provide their error estimates. A detailed discussion on the sharpness of our error bounds and their relation to other results in the literature is given. The techniques used in this paper should also generalize to asymptotic expansions which arise from an application of the method of steepest descents. |
| doi_str_mv | 10.1007/s10440-017-0099-0 |
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Optimization</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Derivatives</topic><topic>Errors</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Representations</topic><topic>Sharpness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nemes, Gergő</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Acta applicandae mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nemes, Gergő</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions</atitle><jtitle>Acta applicandae mathematicae</jtitle><stitle>Acta Appl Math</stitle><date>2017-08-01</date><risdate>2017</risdate><volume>150</volume><issue>1</issue><spage>141</spage><epage>177</epage><pages>141-177</pages><issn>0167-8019</issn><eissn>1572-9036</eissn><abstract>In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. 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| subjects | Applications of Mathematics Asymptotic methods Asymptotic properties Asymptotic series Bessel functions Calculus of Variations and Optimal Control Optimization Computational Mathematics and Numerical Analysis Derivatives Errors Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes Representations Sharpness |
| title | Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions |
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