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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
DOI: https://doi.org/10.1090/S0002-9947-1988-0924765-4
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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Keywords: Lagrange inversion formula, <IMG WIDTH="15" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$q$">-Lagrange inversion formula, inverse relations, umbral operators, <IMG WIDTH="15" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$q$">-exponential function, <IMG WIDTH="15" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img3.gif" ALT="$q$">-Catalan numbers
Article copyright: © Copyright 1988 American Mathematical Society