论文标题
正式力量系列的邀请
An invitation to formal power series
论文作者
论文摘要
这是关于正式权力序列理论的演讲，完全没有任何分析机制。结合了各种作者的想法，我们能够证明牛顿的二项式定理，雅各比的三重产品，罗杰斯 - 罗杰斯 - 罗曼努扬身份以及许多其他突出的结果。我们应用这些方法来得出几种组合定理，包括Ramanujan的分区一致性，生成Stirling数字的功能和Jacobi的四平方定理。我们进一步讨论了正式的Laurent系列和多元电源系列，并以Macmahon的Master Therorem的证明结尾。
This is a lecture on the theory of formal power series developed entirely without any analytic machinery. Combining ideas from various authors we are able to prove Newton's binomial theorem, Jacobi's triple product, the Rogers--Ramanujan identities and many other prominent results. We apply these methods to derive several combinatorial theorems including Ramanujan's partition congruences, generating functions of Stirling numbers and Jacobi's four-square theorem. We further discuss formal Laurent series and multivariate power series and end with a proof of MacMahon's master theorem.
