{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T06:18:18Z","timestamp":1780985898589,"version":"3.54.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T00:00:00Z","timestamp":1714608000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T00:00:00Z","timestamp":1714608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY22A010002"],"award-info":[{"award-number":["LY22A010002"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001280"],"award-info":[{"award-number":["12001280"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971138,11301125"],"award-info":[{"award-number":["11971138,11301125"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s10444-024-10134-7","type":"journal-article","created":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T08:01:49Z","timestamp":1714636909000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fast numerical integration of highly oscillatory Bessel transforms with a Cauchy type singular point and exotic oscillators"],"prefix":"10.1007","volume":"50","author":[{"given":"Hongchao","family":"Kang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guidong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,5,2]]},"reference":[{"key":"10134_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791246","volume-title":"Complex Variables: Introduction and Applications","author":"MJ Ablowitz","year":"2003","unstructured":"Ablowitz, M.J., Fokas, A.S.: Complex Variables: Introduction and Applications. Cambridge University Press, NewYork (2003)"},{"key":"10134_CR2","volume-title":"Handbook of Mathematical Functions","author":"M Abramowitz","year":"1964","unstructured":"Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C (1964)"},{"key":"10134_CR3","volume-title":"Mathematical Methods for Physicists, third","author":"G Arfken","year":"1985","unstructured":"Arfken, G.: Mathematical Methods for Physicists, third. Academic Press, Orlando, FL (1985)"},{"issue":"2","key":"10134_CR4","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1137\/S1064827503428539","volume":"27","author":"G Bao","year":"2005","unstructured":"Bao, G., Sun, W.: A fast algorithm for the electromagnetic scattering from a large cavity. SIAM J. Sci. Comput. 27(2), 553\u2013574 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"10134_CR5","volume-title":"Higher Transcendental Functions, I","author":"H Bateman","year":"1981","unstructured":"Bateman, H., Erd\u00e9lyi, A.: Higher Transcendental Functions, I. Krieger, New York (1981)"},{"key":"10134_CR6","volume-title":"Open problems in the computational solution of Volterra functional equations with highly oscillatory kernels","author":"H Brunner","year":"2007","unstructured":"Brunner, H.: Open problems in the computational solution of Volterra functional equations with highly oscillatory kernels. Effective Computational Methods for Highly Oscillatory Solutions, Isaac Newton Institute, HOP (2007)"},{"key":"10134_CR7","unstructured":"Brunner, H.: On the numerical solution of first-kind Volterra integral equations with highly oscillatory kernels, Isaac Newton Institute. HOP: Highly Oscillatory Problems: From Theory to Applications, pp 13\u201317 (2010)"},{"issue":"5","key":"10134_CR8","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1016\/j.apnum.2012.01.009","volume":"62","author":"R Chen","year":"2012","unstructured":"Chen, R.: Numerical approximations to integrals with a highly oscillatory Bessel kernel. Appl. Numer. Math. 62(5), 636\u2013648 (2012)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"10134_CR9","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10440-012-9709-z","volume":"123","author":"R Chen","year":"2013","unstructured":"Chen, R.: Fast integration for Cauchy principal value integrals of oscillatory kind. Acta Appl. Math. 123(1), 21\u201330 (2013)","journal-title":"Acta Appl. Math."},{"key":"10134_CR10","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.cam.2013.02.025","volume":"250","author":"R Chen","year":"2013","unstructured":"Chen, R.: On the evaluation of Bessel transformations with the oscillators via asymptotic series of Whittaker functions. J. Comput. Appl. Math. 250, 107\u2013121 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"10134_CR11","doi-asserted-by":"crossref","unstructured":"Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration, second ed., Academic Press (1984)","DOI":"10.1016\/B978-0-12-206360-2.50012-1"},{"issue":"1","key":"10134_CR12","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1137\/1009002","volume":"9","author":"W Gautschi","year":"1967","unstructured":"Gautschi, W.: Computational aspects of three-term recurrence relations. SIAM Rev. 9(1), 24\u201382 (1967)","journal-title":"SIAM Rev."},{"key":"10134_CR13","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.cam.2019.02.012","volume":"358","author":"T Hasegawa","year":"2019","unstructured":"Hasegawa, T., Sugiura, H.: Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm. J. Comput. Appl. Math. 358, 327\u2013342 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"10134_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2014.11.023","volume":"280","author":"G He","year":"2015","unstructured":"He, G., Xiang, S.: An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application. J. Comput. Appl. Math. 280, 1\u201313 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"10134_CR15","unstructured":"https:\/\/functions.wolfram.com\/HypergeometricFunctions\/HypergeometricPFQ\/06\/02\/02\/"},{"key":"10134_CR16","unstructured":"http:\/\/functions.wolfram.com\/HypergeometricFunctions\/MeijerG\/21\/02\/07\/0004\/"},{"key":"10134_CR17","unstructured":"http:\/\/functions.wolfram.com\/07.34.06.0031.02"},{"issue":"6","key":"10134_CR18","doi-asserted-by":"publisher","first-page":"2305","DOI":"10.1137\/060651525","volume":"29","author":"D Huybrechs","year":"2007","unstructured":"Huybrechs, D., Vandewalle, S.: A sparse discretization for integral equation formulations of high frequency scattering problems. SIAM J. Sci. Comput. 29(6), 2305\u20132328 (2007)","journal-title":"SIAM J. Sci. Comput."},{"key":"10134_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114835","volume":"420","author":"H Kang","year":"2023","unstructured":"Kang, H., Zhang, M.: Numerical evaluation and analysis of highly oscillatory singular Bessel transforms with a particular oscillator. J. Comput. Appl. Math. 420, 114835 (2023)","journal-title":"J. Comput. Appl. Math."},{"issue":"9","key":"10134_CR20","first-page":"4988","volume":"218","author":"P Keller","year":"2012","unstructured":"Keller, P.: A practical algorithm for computing Cauchy principal value integrals. Appl. Math. Comput. 218(9), 4988\u20135001 (2012)","journal-title":"Appl. Math. Comput."},{"key":"10134_CR21","doi-asserted-by":"crossref","unstructured":"Lozier, D.W.: Numerical Solution of Linear Difference Equations. Report NBSIR 80-1976, National Bureau of Standerds. Washington, D.C (1980)","DOI":"10.6028\/NBS.IR.80-1976"},{"key":"10134_CR22","volume-title":"Integrals of Bessel Functions","author":"YL Luke","year":"1962","unstructured":"Luke, Y.L.: Integrals of Bessel Functions. McGraw-Hill, New York (1962)"},{"key":"10134_CR23","volume-title":"Chebyshev Polynomials","author":"JC Mason","year":"2003","unstructured":"Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. Chapman and Hall\/CRC, New York (2003)"},{"issue":"179","key":"10134_CR24","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1090\/S0025-5718-1987-0890267-X","volume":"49","author":"GE Okecha","year":"1987","unstructured":"Okecha, G.E.: Quadrature formulae for Cauchy principal value integrals of oscillatory kind. Math. Comp. 49(179), 259\u2013268 (1987)","journal-title":"Math. Comp."},{"key":"10134_CR25","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/BF02166688","volume":"11","author":"J Oliver","year":"1968","unstructured":"Oliver, J.: The numerical solution of linear recurrence relations. Numer. Math. 11, 349\u2013360 (1968)","journal-title":"Numer. Math."},{"key":"10134_CR26","unstructured":"Oreshkin, B.: http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/31490-meijerg\/content\/MeijerG\/MeijerG.m"},{"key":"10134_CR27","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1007\/BF01934465","volume":"23","author":"R Piessens","year":"1983","unstructured":"Piessens, R., Branders, M.: Modified Clenshaw-Curtis method for the computation of Bessel function integrals. BIT Numer. Math. 23, 370\u2013381 (1983)","journal-title":"BIT Numer. Math."},{"key":"10134_CR28","volume-title":"Introduction to Special Functions","author":"Z Wang","year":"2000","unstructured":"Wang, Z., Guo, D.: Introduction to Special Functions. Peking University Press, Beijing (2000)"},{"issue":"5","key":"10134_CR29","first-page":"1886","volume":"215","author":"H Wang","year":"2009","unstructured":"Wang, H., Xiang, S.: Uniform approximations to Cauchy principal value integrals of oscillatory functions. Appl. Math. Comput. 215(5), 1886\u20131894 (2009)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"10134_CR30","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.cam.2009.12.007","volume":"234","author":"H Wang","year":"2010","unstructured":"Wang, H., Xiang, S.: On the evaluation of Cauchy principal value integrals of oscillatory functions. J. Comput. Appl. Math. 234(1), 95\u2013100 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"10134_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2019.123640","volume":"483","author":"H Wang","year":"2020","unstructured":"Wang, H.: A unified framework for asymptotic analysis and computation of finite Hankel transform. J. Math. Anal. Appl. 483, 123640 (2020)","journal-title":"J. Math. Anal. Appl."},{"key":"10134_CR32","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s00211-012-0501-9","volume":"123","author":"H Wang","year":"2013","unstructured":"Wang, H., Zhang, L., Huybrechs, D.: Asymptotic expansions and fast computation of oscillatory Hilbert transforms. Numer. Math. 123, 709\u2013743 (2013)","journal-title":"Numer. Math."},{"key":"10134_CR33","volume-title":"A Course of Modern Analysis","author":"ET Whittaker","year":"1927","unstructured":"Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis. Cambridge University Press, Cambridge (1927)"},{"issue":"2","key":"10134_CR34","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1007\/s10543-007-0127-y","volume":"47","author":"S Xiang","year":"2007","unstructured":"Xiang, S.: Numerical analysis of a fast integration method for highly oscillatory functions. BIT Numer. Math. 47(2), 469\u2013482 (2007)","journal-title":"BIT Numer. Math."},{"issue":"9","key":"10134_CR35","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1016\/j.apnum.2007.07.002","volume":"58","author":"S Xiang","year":"2008","unstructured":"Xiang, S., Gui, W., Mo, P.: Numerical quadrature for Bessel transformations. Appl. Numer. Math. 58(9), 1247\u20131261 (2008)","journal-title":"Appl. Numer. Math."},{"issue":"270","key":"10134_CR36","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1090\/S0025-5718-09-02279-0","volume":"79","author":"S Xiang","year":"2010","unstructured":"Xiang, S., Wang, H.: Fast integration of highly oscillatory integrals with exotic oscillators. Math. Comp. 79(270), 829\u2013844 (2010)","journal-title":"Math. Comp."},{"key":"10134_CR37","doi-asserted-by":"publisher","first-page":"1281","DOI":"10.1093\/imanum\/drq035","volume":"31","author":"S Xiang","year":"2011","unstructured":"Xiang, S., Cho, Y.J., Wang, H., Brunner, H.: Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications. IMA J. Numer. Anal. 31, 1281\u20131314 (2011)","journal-title":"IMA J. Numer. Anal."},{"key":"10134_CR38","doi-asserted-by":"publisher","first-page":"1480","DOI":"10.1093\/imanum\/drs052","volume":"33","author":"S Xiang","year":"2013","unstructured":"Xiang, S., Cho, Y.J., Wang, H., Brunner, H.: Erratum to \" Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications \" ( IMA Journal of Numerical Analysis (2011) 31: 1281\u20131314). IMA J. Numer. Anal. 33, 1480\u20131483 (2013)","journal-title":"IMA J. Numer. Anal."},{"key":"10134_CR39","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.cam.2013.08.031","volume":"258","author":"Z Xu","year":"2014","unstructured":"Xu, Z., Xiang, S., He, G.: Efficient evaluation of oscillatory Bessel Hilbert transforms. J. Comput. Appl. Math. 258, 57\u201366 (2014)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-024-10134-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-024-10134-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-024-10134-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T12:13:27Z","timestamp":1719922407000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-024-10134-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,2]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["10134"],"URL":"https:\/\/doi.org\/10.1007\/s10444-024-10134-7","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,2]]},"assertion":[{"value":"27 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"40"}}