{"title":"A study of Horn matrix functions and Horn confluent matrix functions","authors":"Ravi Dwivedi, Ashish Verma","doi":"10.1515/anly-2023-0057","DOIUrl":null,"url":null,"abstract":"\n In this paper, we give the matrix version of Horn’s hypergeometric function and their confluent cases. We also discuss the regions of convergence, system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions. With the study of these 23 matrix functions, matrix generalization of Horn’s list of 34 hypergeometric series will be completed.","PeriodicalId":47773,"journal":{"name":"ANALYSIS","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ANALYSIS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/anly-2023-0057","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we give the matrix version of Horn’s hypergeometric function and their confluent cases. We also discuss the regions of convergence, system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions. With the study of these 23 matrix functions, matrix generalization of Horn’s list of 34 hypergeometric series will be completed.
期刊介绍:
Analysis is the most established and esteemed forum in which to publish short discussions of topics in philosophy. Articles published in Analysis lend themselves to the presentation of cogent but brief arguments for substantive conclusions, and often give rise to discussions which continue over several interchanges. A wide range of topics are covered including: philosophical logic and philosophy of language, metaphysics, epistemology, philosophy of mind, and moral philosophy.