{"title":"单位圆上的超几何Sobolev正交多项式族","authors":"S. Zagorodnyuk","doi":"10.33205/cma.690236","DOIUrl":null,"url":null,"abstract":"In this paper we study the following family of hypergeometric polynomials: $y_n(x) = \\frac{ (-1)^\\rho }{ n! } x^n {}_2 F_0(-n,\\rho;-;-\\frac{1}{x})$, depending on a parameter $\\rho\\in\\mathbb{N}$. Differential equations of orders $\\rho+1$ and $2$ for these polynomials are given. A recurrence relation for $y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2020-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle\",\"authors\":\"S. Zagorodnyuk\",\"doi\":\"10.33205/cma.690236\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study the following family of hypergeometric polynomials: $y_n(x) = \\\\frac{ (-1)^\\\\rho }{ n! } x^n {}_2 F_0(-n,\\\\rho;-;-\\\\frac{1}{x})$, depending on a parameter $\\\\rho\\\\in\\\\mathbb{N}$. Differential equations of orders $\\\\rho+1$ and $2$ for these polynomials are given. A recurrence relation for $y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure.\",\"PeriodicalId\":36038,\"journal\":{\"name\":\"Constructive Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2020-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Constructive Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33205/cma.690236\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Constructive Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33205/cma.690236","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle
In this paper we study the following family of hypergeometric polynomials: $y_n(x) = \frac{ (-1)^\rho }{ n! } x^n {}_2 F_0(-n,\rho;-;-\frac{1}{x})$, depending on a parameter $\rho\in\mathbb{N}$. Differential equations of orders $\rho+1$ and $2$ for these polynomials are given. A recurrence relation for $y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure.