{"title":"关于自旋加权球方程特征值的渐近性","authors":"V. S. Otchik","doi":"10.33581/1561-4085-2022-25-4-368-376","DOIUrl":null,"url":null,"abstract":"Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.","PeriodicalId":43601,"journal":{"name":"Nonlinear Phenomena in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Asymptotics of Eigenvalues of the Spin-Weighted Spheroidal Equation\",\"authors\":\"V. S. Otchik\",\"doi\":\"10.33581/1561-4085-2022-25-4-368-376\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.\",\"PeriodicalId\":43601,\"journal\":{\"name\":\"Nonlinear Phenomena in Complex Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Phenomena in Complex Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33581/1561-4085-2022-25-4-368-376\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Phenomena in Complex Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33581/1561-4085-2022-25-4-368-376","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
On the Asymptotics of Eigenvalues of the Spin-Weighted Spheroidal Equation
Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.
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