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A Noncommutative Generalization and $q$-Analog of the Lagrange Inversion Formula

Ira Gessel
Transactions of the American Mathematical Society
Vol. 257, No. 2 (Feb., 1980), pp. 455-482
DOI: 10.2307/1998307
Stable URL: http://www.jstor.org/stable/1998307
Page Count: 28
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A Noncommutative Generalization and $q$-Analog of the Lagrange Inversion Formula
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Abstract

The Lagrange inversion formula is generalized to formal power series in noncommutative variables. A $q$-analog is obtained by applying a linear operator to the noncommutative formula before substituting commuting variables.

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