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Identities in combinatorics. II. A $ q$-analog of the Lagrange inversion theorem


Author: George E. Andrews
Journal: Proc. Amer. Math. Soc. 53 (1975), 240-245
MSC: Primary 05A10
DOI: https://doi.org/10.1090/S0002-9939-1975-0389610-3
MathSciNet review: 0389610
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Abstract: A $ q$-analog of Lagrange's inversion theorem is obtained. It is applied to give a new proof of an expansion theorem due to Carlitz and to obtain formulae for certain combinatorial numbers studied by Carlitz.


References [Enhancements On Off] (What's this?)

  • [1] T. J. I'A. Bromwich, An introduction to the theory of infinite series, 2nd ed., MacMillan, London, 1959.
  • [2] L. Carlitz, Sequences, paths, ballot numbers, Fibonacci Quart. 10 (1972), no. 5, 531–549. MR 0317949
  • [3] L. Carlitz, Some 𝑞-expansion formulas, Glasnik Mat. Ser. III 8(28) (1973), 205–214 (English, with Serbo-Croatian summary). MR 0330842
  • [4] -, Problem: $ q$-analog of the Lagrange expansion, from Abstracts and Problems from the Conference on Eulerian Series and Applications, May 1974, Pennsylvania State University.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0389610-3
Keywords: Lagrange inversion formula, $ q$-analogs, Catalan numbers
Article copyright: © Copyright 1975 American Mathematical Society