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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Operator methods and Lagrange inversion: a unified approach to Lagrange formulas


Author: Ch. Krattenthaler
Journal: Trans. Amer. Math. Soc. 305 (1988), 431-465
MSC: Primary 05A30; Secondary 05A17, 11P57
MathSciNet review: 924765
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Abstract: We present a general method of proving Lagrange inversion formulas and give new proofs of the $ s$-variable Lagrange-Good formula [13] and the $ q$-Lagrange formulas of Garsia [7], Gessel [10], Gessel and Stanton [11, 12] and the author [18]. We also give some $ q$-analogues of the Lagrange formula in several variables.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0924765-4
PII: S 0002-9947(1988)0924765-4
Keywords: Lagrange inversion formula, $ q$-Lagrange inversion formula, inverse relations, umbral operators, $ q$-exponential function, $ q$-Catalan numbers
Article copyright: © Copyright 1988 American Mathematical Society