{"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}
引用次数: 0
Abstract
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
