{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T05:09:55Z","timestamp":1781154595732,"version":"3.54.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T00:00:00Z","timestamp":1688601600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T00:00:00Z","timestamp":1688601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2021QA023"],"award-info":[{"award-number":["ZR2021QA023"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171284"],"award-info":[{"award-number":["12171284"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["MOE-Tier1-RG15\/21"],"award-info":[{"award-number":["MOE-Tier1-RG15\/21"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["12131005"],"award-info":[{"award-number":["12131005"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["11871145"],"award-info":[{"award-number":["11871145"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971016"],"award-info":[{"award-number":["11971016"]}],"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":["12201385"],"award-info":[{"award-number":["12201385"]}],"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":["12271365"],"award-info":[{"award-number":["12271365"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Pujiang Program","award":["21PJ1403500"],"award-info":[{"award-number":["21PJ1403500"]}]},{"name":"Shanghai Post-doctoral Excellence Program","award":["2021154"],"award-info":[{"award-number":["2021154"]}]},{"DOI":"10.13039\/501100012476","name":"Fundamental Research Funds for Central Universities of the Central South University","doi-asserted-by":"publisher","award":["2021110474"],"award-info":[{"award-number":["2021110474"]}],"id":[{"id":"10.13039\/501100012476","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s10915-023-02254-x","type":"journal-article","created":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T05:01:48Z","timestamp":1688619708000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["M\u00fcntz Ball Polynomials and M\u00fcntz Spectral-Galerkin Methods for Singular Eigenvalue Problems"],"prefix":"10.1007","volume":"96","author":[{"given":"Xiu","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li-Lian","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huiyuan","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changtao","family":"Sheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,6]]},"reference":[{"key":"2254_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325937","volume-title":"Special Functions","author":"GE Andrews","year":"1999","unstructured":"Andrews, G.E., Askey, R., Roy, R.: Special Functions, vol. 71. Cambridge University Press, Cambridge (1999)"},{"key":"2254_CR2","doi-asserted-by":"publisher","DOI":"10.1201\/9780429344374","volume-title":"Spectral Methods Using Multivariate Polynomials on the Unit Ball","author":"K Atkinson","year":"2019","unstructured":"Atkinson, K., Chien, D., Hansen, O.: Spectral Methods Using Multivariate Polynomials on the Unit Ball. CRC Press, Boca Raton (2019)"},{"key":"2254_CR3","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.jat.2014.03.016","volume":"193","author":"L Cagliero","year":"2015","unstructured":"Cagliero, L., Koornwinder, T.H.: Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials. J. Approx. Theory 193, 20\u201338 (2015)","journal-title":"J. Approx. Theory"},{"key":"2254_CR4","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1016\/j.jde.2005.07.010","volume":"224","author":"D Cao","year":"2006","unstructured":"Cao, D., Han, P.: Solutions to critical elliptic equations with multi-singular inverse square potentials. J. Differ. Equ. 224, 332\u2013372 (2006)","journal-title":"J. Differ. Equ."},{"key":"2254_CR5","unstructured":"Cheney, E.W.: Introduction to Approximation Theory, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second edition (1982)"},{"key":"2254_CR6","volume-title":"An Introduction to Orthogonal Polynomials","author":"TS Chihara","year":"1978","unstructured":"Chihara, T.S.: An Introduction to Orthogonal Polynomials, vol. 13. Gordon and Breach Science Publishers, New York (1978)"},{"key":"2254_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6660-4","volume-title":"Approximation Theory and Harmonic Analysis on Spheres and Balls","author":"F Dai","year":"2013","unstructured":"Dai, F., Xu, Y.: Approximation Theory and Harmonic Analysis on Spheres and Balls. Springer, New York (2013)"},{"key":"2254_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107786134","volume-title":"Orthogonal Polynomials of Several Variables. Encyclopedia of Mathematics and its Applications","author":"CF Dunkl","year":"2014","unstructured":"Dunkl, C.F., Xu, Y.: Orthogonal Polynomials of Several Variables. Encyclopedia of Mathematics and its Applications, vol. 155, 2nd edn. Cambridge University Press, Cambridge (2014)","edition":"2"},{"issue":"95","key":"2254_CR9","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1112\/jlms.12024","volume":"2","author":"BO Dyda","year":"2017","unstructured":"Dyda, B.O., Kuznetsov, A., Kwa\u015bnicki, M.: Eigenvalues of the fractional Laplace operator in the unit ball. J. Lond. Math. Soc. 2(95), 500\u2013518 (2017)","journal-title":"J. Lond. Math. Soc."},{"key":"2254_CR10","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/s00365-016-9336-4","volume":"45","author":"BO Dyda","year":"2017","unstructured":"Dyda, B.O., Kuznetsov, A., Kwa\u015bnicki, M.: Fractional Laplace operator and Meijer G-function. Constr. Approx. 45, 427\u2013448 (2017)","journal-title":"Constr. Approx."},{"key":"2254_CR11","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.jfa.2006.10.019","volume":"250","author":"V Felli","year":"2007","unstructured":"Felli, V., Marchini, E.M., Terracini, S.: On Schr\u00f6dinger operators with multipolar inverse-square potentials. J. Funct. Anal. 250, 265\u2013316 (2007)","journal-title":"J. Funct. Anal."},{"key":"2254_CR12","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1080\/03605300500394439","volume":"31","author":"V Felli","year":"2006","unstructured":"Felli, V., Terracini, S.: Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity. Commun. Partial Differ. Equ. 31, 469\u2013495 (2006)","journal-title":"Commun. Partial Differ. Equ."},{"key":"2254_CR13","unstructured":"Kufner, A.: Weighted Sobolev Spaces, A Wiley-Interscience Publication. Wiley, New York, 1985. Translated from the Czech"},{"key":"2254_CR14","doi-asserted-by":"publisher","first-page":"1621","DOI":"10.1090\/S0025-5718-09-02308-4","volume":"79","author":"H Li","year":"2010","unstructured":"Li, H., Shen, J.: Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle. Math. Comput. 79, 1621\u20131646 (2010)","journal-title":"Math. Comput."},{"key":"2254_CR15","doi-asserted-by":"publisher","first-page":"2647","DOI":"10.1137\/130940591","volume":"52","author":"H Li","year":"2014","unstructured":"Li, H., Xu, Y.: Spectral approximation on the unit ball. SIAM J. Numer. Anal. 52, 2647\u20132675 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"2254_CR16","doi-asserted-by":"publisher","first-page":"A114","DOI":"10.1137\/16M1069596","volume":"39","author":"H Li","year":"2017","unstructured":"Li, H., Zhang, Z.: Efficient spectral and spectral element methods for eigenvalue problems of Schr\u00f6dinger equations with an inverse square potential. SIAM J. Sci. Comput. 39, A114\u2013A140 (2017)","journal-title":"SIAM J. Sci. Comput."},{"key":"2254_CR17","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s10915-018-0721-y","volume":"77","author":"S Ma","year":"2018","unstructured":"Ma, S., Li, H., Zhang, Z.: Efficient spectral methods for some singular eigenvalue problems. J. Sci. Comput. 77, 657\u2013688 (2018)","journal-title":"J. Sci. Comput."},{"key":"2254_CR18","doi-asserted-by":"publisher","first-page":"2847","DOI":"10.1090\/mcom\/3544","volume":"89","author":"S Olver","year":"2020","unstructured":"Olver, S., Xu, Y.: Orthogonal polynomials in and on a quadratic surface of revolution. Math. Comput. 89, 2847\u20132865 (2020)","journal-title":"Math. Comput."},{"key":"2254_CR19","doi-asserted-by":"publisher","first-page":"2141","DOI":"10.1051\/m2an\/2021049","volume":"55","author":"C Sheng","year":"2021","unstructured":"Sheng, C., Ma, S., Li, H., Wang, L.-L., Jia, L.: Nontensorial generalised Hermite spectral methods for PDEs with fractional Laplacian and Schr\u00f6dinger operators. ESAIM Math. Model. Numer. Anal. 55, 2141\u20132168 (2021)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2254_CR20","unstructured":"Szeg\u0151, G.: Orthogonal Polynomials, vol. XXIII, American Mathematical Society, Providence, R.I., fourth ed (1975)"},{"key":"2254_CR21","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.acha.2018.08.001","volume":"48","author":"J Zhang","year":"2020","unstructured":"Zhang, J., Li, H., Wang, L.-L., Zhang, Z.: Ball prolate spheroidal wave functions in arbitrary dimensions. Appl. Comput. Harmon. Anal. 48, 539\u2013569 (2020)","journal-title":"Appl. Comput. Harmon. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02254-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02254-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02254-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T08:16:30Z","timestamp":1689581790000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02254-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,6]]},"references-count":21,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["2254"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02254-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,6]]},"assertion":[{"value":"12 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"We have no conflicts of interest to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"59"}}