{"title":"连续 -1$-1$超几何正交多项式","authors":"Jonathan Pelletier, Luc Vinet, Alexei Zhedanov","doi":"10.1111/sapm.12728","DOIUrl":null,"url":null,"abstract":"<p>The study of <span></span><math>\n <semantics>\n <mrow>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$-1$</annotation>\n </semantics></math> orthogonal polynomials viewed as <span></span><math>\n <semantics>\n <mrow>\n <mi>q</mi>\n <mo>→</mo>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$q\\rightarrow -1$</annotation>\n </semantics></math> limits of the <span></span><math>\n <semantics>\n <mi>q</mi>\n <annotation>$q$</annotation>\n </semantics></math>-orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the <span></span><math>\n <semantics>\n <mrow>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$-1$</annotation>\n </semantics></math> analog of the <span></span><math>\n <semantics>\n <mi>q</mi>\n <annotation>$q$</annotation>\n </semantics></math>-Askey scheme. A compendium of the properties of all the continuous <span></span><math>\n <semantics>\n <mrow>\n <mo>−</mo>\n <mn>1</mn>\n </mrow>\n <annotation>$-1$</annotation>\n </semantics></math> hypergeometric polynomials and their connections is provided.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12728","citationCount":"0","resultStr":"{\"title\":\"Continuous \\n \\n \\n −\\n 1\\n \\n $-1$\\n hypergeometric orthogonal polynomials\",\"authors\":\"Jonathan Pelletier, Luc Vinet, Alexei Zhedanov\",\"doi\":\"10.1111/sapm.12728\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The study of <span></span><math>\\n <semantics>\\n <mrow>\\n <mo>−</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$-1$</annotation>\\n </semantics></math> orthogonal polynomials viewed as <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>q</mi>\\n <mo>→</mo>\\n <mo>−</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$q\\\\rightarrow -1$</annotation>\\n </semantics></math> limits of the <span></span><math>\\n <semantics>\\n <mi>q</mi>\\n <annotation>$q$</annotation>\\n </semantics></math>-orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the <span></span><math>\\n <semantics>\\n <mrow>\\n <mo>−</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$-1$</annotation>\\n </semantics></math> analog of the <span></span><math>\\n <semantics>\\n <mi>q</mi>\\n <annotation>$q$</annotation>\\n </semantics></math>-Askey scheme. A compendium of the properties of all the continuous <span></span><math>\\n <semantics>\\n <mrow>\\n <mo>−</mo>\\n <mn>1</mn>\\n </mrow>\\n <annotation>$-1$</annotation>\\n </semantics></math> hypergeometric polynomials and their connections is provided.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12728\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12728\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12728","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
The study of orthogonal polynomials viewed as limits of the -orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the analog of the -Askey scheme. A compendium of the properties of all the continuous hypergeometric polynomials and their connections is provided.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
