{"title":"扩展分数阶积分，矩阵和统计分布的乘积和比率","authors":"A. M. Mathai","doi":"10.12732/IJAM.V33I1.7","DOIUrl":null,"url":null,"abstract":"For two functions, Mellin convolutions of products and ratios are well-known in the literature. But these for three or more functions is not discussed extensively in the literature. The corresponding matrix transform and M-convolutions are rarely considered in the literature. In this paper, a detailed examination of M-convolutions of products and ratios involving three functions is carried out, pointing out the relevance of the results in different areas such as fractional calculus, especially fractional integrals, and statistical distribution theory. AMS Subject Classification: 26A33, 44A05, 44A35, 62EXX, 62H10, 15B52","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"1 1","pages":"75"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"EXTENDED FRACTIONAL INTEGRALS, PRODUCTS AND RATIOS OF MATRICES AND STATISTICAL DISTRIBUTIONS\",\"authors\":\"A. M. Mathai\",\"doi\":\"10.12732/IJAM.V33I1.7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For two functions, Mellin convolutions of products and ratios are well-known in the literature. But these for three or more functions is not discussed extensively in the literature. The corresponding matrix transform and M-convolutions are rarely considered in the literature. In this paper, a detailed examination of M-convolutions of products and ratios involving three functions is carried out, pointing out the relevance of the results in different areas such as fractional calculus, especially fractional integrals, and statistical distribution theory. AMS Subject Classification: 26A33, 44A05, 44A35, 62EXX, 62H10, 15B52\",\"PeriodicalId\":14365,\"journal\":{\"name\":\"International journal of pure and applied mathematics\",\"volume\":\"1 1\",\"pages\":\"75\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of pure and applied mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/IJAM.V33I1.7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of pure and applied mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/IJAM.V33I1.7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
EXTENDED FRACTIONAL INTEGRALS, PRODUCTS AND RATIOS OF MATRICES AND STATISTICAL DISTRIBUTIONS
For two functions, Mellin convolutions of products and ratios are well-known in the literature. But these for three or more functions is not discussed extensively in the literature. The corresponding matrix transform and M-convolutions are rarely considered in the literature. In this paper, a detailed examination of M-convolutions of products and ratios involving three functions is carried out, pointing out the relevance of the results in different areas such as fractional calculus, especially fractional integrals, and statistical distribution theory. AMS Subject Classification: 26A33, 44A05, 44A35, 62EXX, 62H10, 15B52
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