{"title":"通过拉曼努强主定理论有限梅林变换","authors":"Omprakash Atale","doi":"arxiv-2409.06304","DOIUrl":null,"url":null,"abstract":"This paper aims to show that by making use of Ramanujan's Master Theorem and\nthe properties of the lower incomplete gamma function, it is possible to\nconstruct a finite Mellin transform for the function $f(x)$ that has infinite\nseries expansions in positive integral powers of $x$. Some applications are\ndiscussed by evaluating certain definite integrals. The obtained solutions are\nalso compared with results from Mathematica to test the validity of the\ncalculations.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Finite Mellin Transform via Ramanujan's Master Theorem\",\"authors\":\"Omprakash Atale\",\"doi\":\"arxiv-2409.06304\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper aims to show that by making use of Ramanujan's Master Theorem and\\nthe properties of the lower incomplete gamma function, it is possible to\\nconstruct a finite Mellin transform for the function $f(x)$ that has infinite\\nseries expansions in positive integral powers of $x$. Some applications are\\ndiscussed by evaluating certain definite integrals. The obtained solutions are\\nalso compared with results from Mathematica to test the validity of the\\ncalculations.\",\"PeriodicalId\":501502,\"journal\":{\"name\":\"arXiv - MATH - General Mathematics\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - General Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06304\",\"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 - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06304","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Finite Mellin Transform via Ramanujan's Master Theorem
This paper aims to show that by making use of Ramanujan's Master Theorem and
the properties of the lower incomplete gamma function, it is possible to
construct a finite Mellin transform for the function $f(x)$ that has infinite
series expansions in positive integral powers of $x$. Some applications are
discussed by evaluating certain definite integrals. The obtained solutions are
also compared with results from Mathematica to test the validity of the
calculations.
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