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Analytic aspects of the shuffle product Mishna, Marni Zabrocki, Mike Generating functions formal languages shuffle product There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences, we find that the shuffle product models many key aspects of D-finite generating functions, a class which contains algebraic. We consider several different takes on the shuffle product, shuffle closure, and shuffle grammars, and give explicit generating function consequences. In the process, we define a grammar class that models D-finite generating functions. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marni Mishna and Mike Zabrocki 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1317 urn:nbn:de:0030-drops-13178 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1317 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode