{"title":"On the gamma transform and its applications","authors":"Slobodan B. Tričković, Miomir S. Stanković","doi":"arxiv-2407.13812","DOIUrl":null,"url":null,"abstract":"We make use of the Laplace transform and gamma function to construct a new\nintegral transform having the property of mapping a derivative to the backward\ndifference, whence we derive a method for solving difference equations and,\nrelying on classical orthogonal polynomials, for obtaining combinatorial\nidentities. A table of some basic functions is given in the Appendix.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"126 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.13812","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
We make use of the Laplace transform and gamma function to construct a new
integral transform having the property of mapping a derivative to the backward
difference, whence we derive a method for solving difference equations and,
relying on classical orthogonal polynomials, for obtaining combinatorial
identities. A table of some basic functions is given in the Appendix.
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