{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:53:12Z","timestamp":1759117992463,"version":"3.37.3"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T00:00:00Z","timestamp":1581379200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T00:00:00Z","timestamp":1581379200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s11786-020-00458-0","type":"journal-article","created":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T11:03:01Z","timestamp":1581418981000},"page":"623-640","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Calculation and Properties of Zonal Polynomials"],"prefix":"10.1007","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9032-513X","authenticated-orcid":false,"given":"Lin","family":"Jiu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1135-3082","authenticated-orcid":false,"given":"Christoph","family":"Koutschan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,11]]},"reference":[{"key":"458_CR1","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s11222-009-9154-7","volume":"21","author":"R Butler","year":"2011","unstructured":"Butler, R., Paige, R.: Exact distributional computations for Roy\u2019s statistic and the largest eigenvalue of a Wishart distribution. Stat. Comput. 21, 147\u2013157 (2011)","journal-title":"Stat. Comput."},{"issue":"2","key":"458_CR2","first-page":"781","volume":"301","author":"K Gross","year":"1987","unstructured":"Gross, K., Richards, D.: Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. AMS 301(2), 781\u2013811 (1987)","journal-title":"Trans. AMS"},{"key":"458_CR3","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.jmva.2013.03.011","volume":"117","author":"H Hashiguchi","year":"2013","unstructured":"Hashiguchi, H., Numata, Y., Takayama, N., Takemura, A.: The holonomic gradient method for the distribution function of the largest root of a Wishart matrix. J. Multivar. Anal. 117, 296\u2013312 (2013). https:\/\/doi.org\/10.1016\/j.jmva.2013.03.011","journal-title":"J. Multivar. Anal."},{"key":"458_CR4","volume-title":"Differential Geometry and Symmetric Spaces","author":"S Helgason","year":"1962","unstructured":"Helgason, S.: Differential Geometry and Symmetric Spaces. Academic Press, New York (1962)"},{"key":"458_CR5","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1016\/S0024-3795(16)30306-8","volume":"121","author":"RG J\u00e1imez","year":"1989","unstructured":"J\u00e1imez, R.G., Guti\u00e9rrez, J.A.M.: An application of zonal polynomials to the generalization of probability distributions. Linear Algebra Appl. 121, 610\u2013616 (1989)","journal-title":"Linear Algebra Appl."},{"issue":"5","key":"458_CR6","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1214\/aoms\/1177698153","volume":"39","author":"A James","year":"1968","unstructured":"James, A.: Calculation of zonal polynomial coefficients by use of the Laplace\u2013Beltrami operator. Ann. Math. Stat. 39(5), 1711\u20131718 (1968)","journal-title":"Ann. Math. Stat."},{"issue":"2","key":"458_CR7","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1214\/aos\/1009210544","volume":"29","author":"I Johnstone","year":"2001","unstructured":"Johnstone, I.: On the distribution of the largest eigenvalue in principal components analysis. Ann. Stat. 29(2), 295\u2013327 (2001)","journal-title":"Ann. Stat."},{"key":"458_CR8","unstructured":"Kauers, M.: Guessing handbook. Technical Report 09-07, RISC Report Series, Johannes Kepler University, Linz, Austria (2009). http:\/\/www.risc.jku.at\/research\/combinat\/software\/Guess\/. Accessed 1 Nov 2018"},{"issue":"254","key":"458_CR9","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1090\/S0025-5718-06-01824-2","volume":"75","author":"P Koev","year":"2006","unstructured":"Koev, P., Edelman, A.: The efficient evaluation of the hypergeometric function of a matrix argument. Math. Comput. 75(254), 833\u2013846 (2006)","journal-title":"Math. Comput."},{"key":"458_CR10","unstructured":"Koutschan, C.: HolonomicFunctions (user\u2019s guide). Technical Report 10-01, RISC Report Series, Johannes Kepler University, Linz, Austria (2010). http:\/\/www.risc.jku.at\/research\/combinat\/software\/HolonomicFunctions\/. Accessed 1 Nov 2018"},{"key":"458_CR11","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1016\/0047-259X(84)90038-1","volume":"14","author":"HB Kushner","year":"1984","unstructured":"Kushner, H.B., Meisner, M.: Formulas for zonal polynomials. J. Multivariate Anal. 14, 336\u2013347 (1984)","journal-title":"J. Multivariate Anal."},{"issue":"3","key":"458_CR12","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1137\/S0895479803436937","volume":"26","author":"M Moakher","year":"2005","unstructured":"Moakher, M.: A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 26(3), 735\u2013747 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"458_CR13","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1214\/aoms\/1177696975","volume":"41","author":"R Muirhead","year":"1970","unstructured":"Muirhead, R.: Systems of partial differential equations for hypergeometric functions of matrix argument. Ann. Math. Stat. 41(3), 991\u20131001 (1970). https:\/\/doi.org\/10.1214\/aoms\/1177696975","journal-title":"Ann. Math. Stat."},{"key":"458_CR14","volume-title":"Aspects of Multivariate Statistical Theory. Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics","author":"R Muirhead","year":"1982","unstructured":"Muirhead, R.: Aspects of Multivariate Statistical Theory. Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics. Wiley, New York (1982)"},{"key":"458_CR15","unstructured":"NIST Digital Library of Mathematical Functions. Release 1.0.20 of 2018-09-15. http:\/\/dlmf.nist.gov\/. Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., Saunders, B.V. (eds.)"},{"issue":"3","key":"458_CR16","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1016\/j.aam.2011.03.001","volume":"47","author":"H Nakayama","year":"2011","unstructured":"Nakayama, H., Nishiyama, K., Noro, M., Ohara, K., Sei, T., Takayama, N., Takemura, A.: Holonomic gradient descent and its application to the Fisher-Bingham integral. Adv. Appl. Math. 47(3), 639\u2013658 (2011). https:\/\/doi.org\/10.1016\/j.aam.2011.03.001","journal-title":"Adv. Appl. Math."},{"key":"458_CR17","doi-asserted-by":"publisher","unstructured":"Noro, M.: System of partial differential equations for the hypergeometric function 1F1 of a matrix argument on diagonal regions. In: Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC), ISSAC \u201916, pp. 381\u2013388. ACM, New York, NY, USA (2016). https:\/\/doi.org\/10.1145\/2930889.2930905","DOI":"10.1145\/2930889.2930905"},{"issue":"4","key":"458_CR18","doi-asserted-by":"publisher","first-page":"2322","DOI":"10.1109\/TWC.2014.2385075","volume":"14","author":"C Siriteanu","year":"2015","unstructured":"Siriteanu, C., Takemura, A., Kuriki, S., Shin, H., Koutschan, C.: MIMO zero-forcing performance evaluation using the holonomic gradient method. IEEE Trans. Wirel. Commun. 14(4), 2322\u20132335 (2015). https:\/\/doi.org\/10.1109\/TWC.2014.2385075","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"458_CR19","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1006\/jsco.1995.1077","volume":"20","author":"J Stembridge","year":"1995","unstructured":"Stembridge, J.: A Maple package for symmetric functions. J. Symb. Comput. 20, 755\u2013768 (1995)","journal-title":"J. Symb. Comput."},{"key":"458_CR20","volume-title":"Zonal Polynomials, Institute of Mathematical Statistics Lecture Notes\u2014Monograph Series","author":"A Takemura","year":"1984","unstructured":"Takemura, A.: Zonal Polynomials, Institute of Mathematical Statistics Lecture Notes\u2014Monograph Series. Institute of Mathematical Statistics, Hayward (1984)"},{"issue":"1\u20132","key":"458_CR21","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1093\/biomet\/20A.1-2.32","volume":"20A","author":"J Wishart","year":"1928","unstructured":"Wishart, J.: The generalised product moment distribution in samples from a normal multivariate population. Biometrika 20A(1\u20132), 32\u201352 (1928). https:\/\/doi.org\/10.1093\/biomet\/20A.1-2.32","journal-title":"Biometrika"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-020-00458-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-020-00458-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-020-00458-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T06:35:35Z","timestamp":1612938935000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-020-00458-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,11]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["458"],"URL":"https:\/\/doi.org\/10.1007\/s11786-020-00458-0","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"type":"print","value":"1661-8270"},{"type":"electronic","value":"1661-8289"}],"subject":[],"published":{"date-parts":[[2020,2,11]]},"assertion":[{"value":"1 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 February 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}