{"title":"关于二元杰克多项式的积分积公式","authors":"Béchir Amri","doi":"10.1007/s13370-025-01383-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, we provide an elementary proof of an integral product formula for Jack polynomials of two variables, extending the well-known case of zonal polynomials. As an application, we derive an explicit integral representation for the Dunk- Bessel function of type <span>\\(B_2\\)</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 4","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"About integral product formula for Jack polynomials of two variables\",\"authors\":\"Béchir Amri\",\"doi\":\"10.1007/s13370-025-01383-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work, we provide an elementary proof of an integral product formula for Jack polynomials of two variables, extending the well-known case of zonal polynomials. As an application, we derive an explicit integral representation for the Dunk- Bessel function of type <span>\\\\(B_2\\\\)</span>.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 4\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01383-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01383-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
About integral product formula for Jack polynomials of two variables
In this work, we provide an elementary proof of an integral product formula for Jack polynomials of two variables, extending the well-known case of zonal polynomials. As an application, we derive an explicit integral representation for the Dunk- Bessel function of type \(B_2\).
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