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Lagrange inversion for species

✍ Scribed by Ira M Gessel; Gilbert Labelle


Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
896 KB
Volume
72
Category
Article
ISSN
0097-3165

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Q-Analogues of Lagrange Inversion
✍ D. Singer πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 438 KB

An inversion theorem is proved which places into a common setting and extends the work of Andrews, Gessel, Garsia, and Garsia and Remmel. Examples of \(q\)-Lagrange inversion are given, including new Rogers-Ramanujan type identities. (c) 1995 Academic Press. Inc.

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The original Lagrange inversion formula, which gives explicitly the inverse under composition of a formal series, was obtained by Lagrange in 1770 through formal computations involving logarithms of inlmite products. See Lagrange [ 121. There exists an extensive literature on various versions of th