Lagrange Inversion Formula by Induction

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-09-15 DOI:10.1080/00029890.2023.2251344

Erlang Surya, Lutz Warnke

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

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拉格朗日归纳法反演公式

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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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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