{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T10:59:13Z","timestamp":1785149953415,"version":"3.55.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1007\/s12190-026-02858-0","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T13:10:15Z","timestamp":1783084215000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Moments-based computation of highly oscillatory integrals with exponential and Bessel kernels"],"prefix":"10.1007","volume":"72","author":[{"given":"Ruyun","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Du","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"2858_CR1","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1016\/j.matcom.2025.10.014","volume":"241","author":"S. Khan","year":"2026","unstructured":"Khan, S., Zaman, S., Rehman, S., Wang, B., Qian, Z.: Modified Levin formulation for highly oscillatory Bessel integral transforms. Math. Comput. Simul. 241, 411\u2013430 (2026). https:\/\/doi.org\/10.1016\/j.matcom.2025.10.014","journal-title":"Math. Comput. Simul."},{"key":"2858_CR2","doi-asserted-by":"publisher","first-page":"129671","DOI":"10.1016\/j.amc.2025.129671","volume":"509","author":"M.T. Hanna","year":"2026","unstructured":"Hanna, M.T.: Matrix-based evaluation of the fractional Hankel transform by Bessel series expansion. Appl. Math. Comput. 509, 129671 (2026) 126455.https:\/\/doi.org\/10.1016\/j.amc.2025.129671","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2858_CR3","doi-asserted-by":"publisher","first-page":"105","DOI":"10.56754\/0719-0646.2801.105","volume":"28","author":"H. Mejjaoli","year":"2026","unstructured":"Mejjaoli, H., Shah, F.A., Sraieb, N.: Generalized translation and convolution operators in the realm of linear canonical deformed Hankel transform with applications, CUBO. Cubo (Temuco, Online) 28(1), 105\u2013147 (2026). https:\/\/doi.org\/10.56754\/0719-0646.2801.105","journal-title":"Cubo (Temuco, Online)"},{"key":"2858_CR4","doi-asserted-by":"publisher","first-page":"26958","DOI":"10.3934\/math.20251185","volume":"10","author":"S. Ghobber","year":"2025","unstructured":"Ghobber, S., Mejjaoli, H.: Wavelet multipliers for the linear canonical deformed Hankel transform and applications. Aims Math. 10, 26958\u201326993 (2025)","journal-title":"Aims Math."},{"issue":"158","key":"2858_CR5","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1090\/S0025-5718-1982-0645668-7","volume":"38","author":"D. Levin","year":"1982","unstructured":"Levin, D.: Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations. Math. Comp. 38(158), 531\u2013538 (1982). https:\/\/doi.org\/10.1090\/S0025-5718-1982-0645668-7","journal-title":"Math. Comp."},{"issue":"1","key":"2858_CR6","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/0377-0427(94)00118-9","volume":"67","author":"D. Levin","year":"1996","unstructured":"Levin, D.: Fast integration of rapidly oscillatory functions. J. Comput. Appl. Math. 67(1), 95\u2013101 (1996). https:\/\/doi.org\/10.1016\/0377-0427(94)00118-9","journal-title":"J. Comput. Appl. Math."},{"key":"2858_CR7","doi-asserted-by":"publisher","first-page":"116687","DOI":"10.1016\/j.cam.2025.116687","volume":"470","author":"Y.K. Wang","year":"2025","unstructured":"Wang, Y.K., Xiang, S.H.: Augmented Levin methods for vector-valued highly oscillatory integrals with exotic oscillators and turning points. J. Comput. Appl. Math. 470, 116687 (2025).https:\/\/doi.org\/10.1016\/j.cam.2025.116687","journal-title":"J. Comput. Appl. Math."},{"key":"2858_CR8","doi-asserted-by":"publisher","first-page":"124775","DOI":"10.1016\/j.amc.2019.124775","volume":"367","author":"J.J. Ma","year":"2020","unstructured":"Ma, J.J., Liu, H.L.: A sparse fractional jacobi-galerkin-Levin quadrature rule for highly oscillatory integrals. Appl. Math. Comput. 367, 124775 (2020).https:\/\/doi.org\/10.1016\/j.amc.2019.124775","journal-title":"Appl. Math. Comput."},{"key":"2858_CR9","doi-asserted-by":"publisher","first-page":"129523","DOI":"10.1016\/j.amc.2025.129523","volume":"505","author":"H.C.K. Y.Y.jia","year":"2025","unstructured":"Y.Y.jia, H.C.K.: Numerical methods of oscillatory Bessel transforms with algebraic and cauchy singularities. Appl. Math. Comput. 505, 129523 (2025).https:\/\/doi.org\/10.1016\/j.amc.2025.129523","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"2858_CR10","doi-asserted-by":"publisher","first-page":"1281","DOI":"10.1093\/imanum\/drq035","volume":"31","author":"S.H. Xiang","year":"2011","unstructured":"Xiang, S.H., Cho, Y.J., Wang, H.Y., Brunner, H.: Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications. IMA J. Numer. Anal. 31(4), 1281\u20131314 (2011). https:\/\/doi.org\/10.1093\/imanum\/drq035","journal-title":"IMA J. Numer. Anal."},{"issue":"270","key":"2858_CR11","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1090\/S0025-5718-09-02279-0","volume":"79","author":"S.H. Xiang","year":"2010","unstructured":"Xiang, S.H., Wang, H.Y.: Fast integration of highly oscillatory integrals with exotic oscillators. Math. Comp. 79(270), 829\u2013844 (2010). https:\/\/doi.org\/10.1090\/S0025-5718-09-02279-0","journal-title":"Math. Comp."},{"issue":"1","key":"2858_CR12","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s11075-015-0033-3","volume":"72","author":"Z.H. Xu","year":"2016","unstructured":"Xu, Z.H., Xiang, S.H.: On the evaluation of highly oscillatory finite Hankel transform using special functions. Numer. Algor. 72(1), 37\u201356 (2016). https:\/\/doi.org\/10.1007\/s11075-015-0033-3","journal-title":"Numer. Algor."},{"issue":"5","key":"2858_CR13","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1016\/j.apnum.2012.01.009","volume":"62","author":"R.Y. Chen","year":"2012","unstructured":"Chen, R.Y.: Numerical approximations to integrals with a highly oscillatory Bessel kernel. Appl. Numer. Math. 62(5), 636\u2013648 (2012). https:\/\/doi.org\/10.1016\/j.apnum.2012.01.009","journal-title":"Appl Numer Math."},{"key":"2858_CR14","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.cam.2013.02.025","volume":"250","author":"R.Y. Chen","year":"2013","unstructured":"Chen, R.Y.: On the evaluation of Bessel transformations with the oscillators via asymptotic series of Whittaker functions. J. Comput. Appl. Math. 250, 107\u2013121 (2013). https:\/\/doi.org\/10.1016\/j.cam.2013.02.025","journal-title":"J. Comput. Appl. Math."},{"key":"2858_CR15","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.matcom.2025.04.016","volume":"236","author":"R.Y. Chen","year":"2025","unstructured":"Chen, R.Y., Li, Y., Zhou, Y.X.: Numerical steepest descent method for computing oscillatory-type Bessel integral transforms. Math. Comput. Simul. 236, 320\u2013333 (2025). https:\/\/doi.org\/10.1016\/j.matcom.2025.04.016","journal-title":"Comput. Simul."},{"issue":"2","key":"2858_CR16","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.jmaa.2010.07.012","volume":"372","author":"R.Y. Chen","year":"2010","unstructured":"Chen, R.Y., Liang, X.M.: Asymptotic expansions of Bessel, anger and Weber transformations. J. Math. Anal. Appl. 372(2), 377\u2013389 (2010). https:\/\/doi.org\/10.1016\/j.jmaa.2010.07.012","journal-title":"J. Math. Anal. Appl."},{"issue":"1","key":"2858_CR17","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.amc.2009.04.048","volume":"215","author":"R.Y. Chen","year":"2009","unstructured":"Chen, R.Y., Xiang, S.H.: Note on the homotopy perturbation method for multivariate vector-value oscillatory integrals. Appl. Math. Comput. 215(1), 78\u201384 (2009). https:\/\/doi.org\/10.1016\/j.amc.2009.04.048","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2858_CR18","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1093\/imanum\/draf007","volume":"46","author":"H.Y. Wang","year":"2026","unstructured":"Wang, H.Y., Wu, M.: Complex generalized Gauss-radau quadrature rules for Hankel transforms of integer order. IMA J. Numer. Anal. 46(1), 623\u2013645 (2026). https:\/\/doi.org\/10.1093\/imanum\/draf007","journal-title":"IMA J. Numer. Anal."},{"issue":"6","key":"2858_CR19","doi-asserted-by":"publisher","first-page":"3169","DOI":"10.1093\/imanum\/drac067","volume":"43","author":"G. Maierhofer","year":"2023","unstructured":"Maierhofer, G., Iserles, A., Peake, N.: Recursive moment computation in Filon methods and application to high-frequency wave scattering in two dimensions. IMA J. Numer. Anal. 43(6), 3169\u20133211 (2023). https:\/\/doi.org\/10.1093\/imanum\/drac067","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"2858_CR20","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s10543-025-01079-4","volume":"65","author":"A. Iserles","year":"2025","unstructured":"Iserles, A., Maierhofer, G.: An accelerated Levin-Clenshaw-Curtis method for the evaluation of highly oscillatory integrals. BIT Numer. Math. 65(3), 36 (2025). https:\/\/doi.org\/10.1007\/s10543-025-01079-4","journal-title":"BIT Numer. Math."},{"key":"2858_CR21","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/j.matcom.2025.10.022","volume":"241","author":"H.C. Kang","year":"2026","unstructured":"Kang, H.C., Zhao, P.: Efficient methods and analysis for computing integrals of composite oscillatory functions. Math. Comput. Simulat. 241, 393\u2013410 (2026). https:\/\/doi.org\/10.1016\/j.matcom.2025.10.022","journal-title":"Math. Comput. Simulat."},{"issue":"1","key":"2858_CR22","doi-asserted-by":"publisher","first-page":"130193","DOI":"10.1016\/j.jmaa.2025.130193","volume":"556","author":"X. Hou","year":"2026","unstructured":"Hou, X., Kang, H.C.: Efficient numerical methods for the algebraic singular and hypersingular oscillatory Fourier transform with a special oscillator. J. Math. Anal. Appl. 556(1), 130193 (2026).https:\/\/doi.org\/10.1016\/j.jmaa.2025.130193","journal-title":"J. Math. Anal. Appl."},{"key":"2858_CR23","doi-asserted-by":"crossref","unstructured":"Gao, J.: Asymptotic expansion of the integral with two oscillations on an infinite interval. Nonlinear Anal. 213 (2021) 112503","DOI":"10.1016\/j.na.2021.112503"},{"key":"2858_CR24","volume-title":"Table of Integrals, Series and Products","author":"I.S. Gradshteyn","year":"1994","unstructured":"Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series and products, 5th edn. Academic, New York (1994). https:\/\/functions.wolfram.com\/HypergeometricFunctions\/Hypergeometric2F1\/06\/01\/03\/01\/01\/0003\/","edition":"5th"},{"key":"2858_CR25","unstructured":"https:\/\/functions.wolfram.com\/HypergeometricFunctions\/Hypergeometric2F1\/06\/01\/05\/01\/02\/0002\/"},{"key":"2858_CR26","unstructured":"https:\/\/functions.wolfram.com\/Bessel-TypeFunctions\/BesselJ\/06\/01\/04\/01\/01\/0003\/"},{"key":"2858_CR27","volume-title":"Methods of Numerical Integration","author":"P.J. Davis","year":"1984","unstructured":"Davis, P.J., Rabinowitz, P.: Methods of numerical integration, 2nd edn. Academic, Orlando, Florida (1984)","edition":"2nd"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-026-02858-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-026-02858-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-026-02858-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T10:02:08Z","timestamp":1785146528000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-026-02858-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":27,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["2858"],"URL":"https:\/\/doi.org\/10.1007\/s12190-026-02858-0","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7]]},"assertion":[{"value":"21 March 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflict of interest.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"199"}}