{"title":"雅可比多项式积积分的一个渐近公式","authors":"Maxim S. Derevyagin, Nicholas Juricic","doi":"10.31390/JOSA.1.4.08","DOIUrl":null,"url":null,"abstract":"We recast Byerly's formula for integrals of products of Legendre polynomials. Then we adopt the idea to the case of Jacobi polynomials. After that, we use the formula to derive an asymptotic formula for integrals of products of Jacobi polynomials. The asymptotic formula is similar to an analogous one recently obtained by the first author and Jeff Geronimo for a different case. Thus, it suggests that such an asymptotic behavior is rather generic for integrals of products of orthogonal polynomials.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"An Asymptotic Formula for Integrals of Products of Jacobi Polynomials\",\"authors\":\"Maxim S. Derevyagin, Nicholas Juricic\",\"doi\":\"10.31390/JOSA.1.4.08\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We recast Byerly's formula for integrals of products of Legendre polynomials. Then we adopt the idea to the case of Jacobi polynomials. After that, we use the formula to derive an asymptotic formula for integrals of products of Jacobi polynomials. The asymptotic formula is similar to an analogous one recently obtained by the first author and Jeff Geronimo for a different case. Thus, it suggests that such an asymptotic behavior is rather generic for integrals of products of orthogonal polynomials.\",\"PeriodicalId\":8451,\"journal\":{\"name\":\"arXiv: Classical Analysis and ODEs\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Classical Analysis and ODEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31390/JOSA.1.4.08\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31390/JOSA.1.4.08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An Asymptotic Formula for Integrals of Products of Jacobi Polynomials
We recast Byerly's formula for integrals of products of Legendre polynomials. Then we adopt the idea to the case of Jacobi polynomials. After that, we use the formula to derive an asymptotic formula for integrals of products of Jacobi polynomials. The asymptotic formula is similar to an analogous one recently obtained by the first author and Jeff Geronimo for a different case. Thus, it suggests that such an asymptotic behavior is rather generic for integrals of products of orthogonal polynomials.
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
