Identities in combinatorics. II. A $q$-analog of the Lagrange inversion theorem
HTML articles powered by AMS MathViewer
- by George E. Andrews PDF
- Proc. Amer. Math. Soc. 53 (1975), 240-245 Request permission
Abstract:
A $q$-analog of Lagrangeโs 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
-
T. J. IโA. Bromwich, An introduction to the theory of infinite series, 2nd ed., MacMillan, London, 1959.
- L. Carlitz, Sequences, paths, ballot numbers, Fibonacci Quart. 10 (1972), no.ย 5, 531โ549. MR 317949
- L. Carlitz, Some $q$-expansion formulas, Glasnik Mat. Ser. III 8(28) (1973), 205โ214 (English, with Serbo-Croatian summary). MR 330842 โ, Problem: $q$-analog of the Lagrange expansion, from Abstracts and Problems from the Conference on Eulerian Series and Applications, May 1974, Pennsylvania State University.
Additional Information
- © Copyright 1975 American Mathematical Society
- 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