{"title":"Lagrange Inversion Formula by Induction","authors":"Erlang Surya, Lutz Warnke","doi":"10.1080/00029890.2023.2251344","DOIUrl":null,"url":null,"abstract":"AbstractWe present a simple inductive proof of the Lagrange Inversion Formula.MSC:: 05A15 AcknowledgmentWe are very grateful to Ira Gessel for several helpful comments and simplifications. We thank Juanjo Rué for suggesting the t-ary tree example (Equation8(8) A(x)=x(1+At(x)).(8) ), and the referees for pointing out additional references. This work was supported by NSF CAREER grant DMS-2225631 and a Sloan Research Fellowship.Additional informationFundingAlfred P. Sloan Foundation; Directorate for Mathematical and Physical Sciences","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2251344","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
AbstractWe present a simple inductive proof of the Lagrange Inversion Formula.MSC:: 05A15 AcknowledgmentWe are very grateful to Ira Gessel for several helpful comments and simplifications. We thank Juanjo Rué for suggesting the t-ary tree example (Equation8(8) A(x)=x(1+At(x)).(8) ), and the referees for pointing out additional references. This work was supported by NSF CAREER grant DMS-2225631 and a Sloan Research Fellowship.Additional informationFundingAlfred P. Sloan Foundation; Directorate for Mathematical and Physical Sciences
摘要给出了拉格朗日反演公式的一个简单的归纳证明。我们非常感谢Ira Gessel提供的一些有用的评论和简化。我们感谢Juanjo ru提出的t-ary树的例子(方程8(8)A(x)=x(1+At(x)).(8))，并感谢推荐人指出了额外的参考文献。这项工作得到了美国国家科学基金会职业基金DMS-2225631和斯隆研究奖学金的支持。alfred P. Sloan基金会;数学和物理科学理事会
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