{"title":"劳里切拉函数的一些无限展开及其在奇异椭圆方程基本解研究中的应用","authors":"T. G. Ergashev, A. Hasanov, T. K. Yuldashev","doi":"10.1134/s1995080224600742","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article, a new inverse pair of symbolic operators with\nthe multidimensional analogues is introduced. The properties of\ninverse pair of symbolic operators with the multidimensional\nanalogues are studied. Formulas for the infinite expansion of\nmultiple Lauricella functions are established. The application of\nsome expansions in studying the properties of fundamental\nsolutions of singular elliptic equations is shown.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation\",\"authors\":\"T. G. Ergashev, A. Hasanov, T. K. Yuldashev\",\"doi\":\"10.1134/s1995080224600742\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this article, a new inverse pair of symbolic operators with\\nthe multidimensional analogues is introduced. The properties of\\ninverse pair of symbolic operators with the multidimensional\\nanalogues are studied. Formulas for the infinite expansion of\\nmultiple Lauricella functions are established. The application of\\nsome expansions in studying the properties of fundamental\\nsolutions of singular elliptic equations is shown.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224600742\",\"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":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224600742","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation
Abstract
In this article, a new inverse pair of symbolic operators with
the multidimensional analogues is introduced. The properties of
inverse pair of symbolic operators with the multidimensional
analogues are studied. Formulas for the infinite expansion of
multiple Lauricella functions are established. The application of
some expansions in studying the properties of fundamental
solutions of singular elliptic equations is shown.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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