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The β‐Extension of the Multivariable Lagrange Inversion Formula
Author(s) -
Zeng Jiang
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1991842167
Subject(s) - multivariable calculus , extension (predicate logic) , inversion (geology) , mathematics , identity (music) , algebra over a field , combinatorial proof , pure mathematics , calculus (dental) , combinatorics , computer science , physics , geology , medicine , paleontology , dentistry , structural basin , control engineering , acoustics , engineering , programming language
We show that Gessel's combinatorial proof of the multivariable Lagrange inversion formula can be given a ,β‐extension, which generalizes Foata and Zeilberger's, β‐extension of MacMahon's master theorem. Moreover, we show that there is no need to use Jacobi's identity in the derivation of the Lagrange formula. Finally, combining Gessel's method and ours, we obtain a new proof of Jacobi's identity.