Planar Trees and the Lagrange Inversion Formula

2021 ◽  
pp. 133-179
Author(s):  
Ömer Eğecioğlu ◽  
Adriano M. Garsia
Keyword(s):  
Inversion Formula ◽  
Lagrange Inversion ◽  
Lagrange Inversion Formula

scholarly journals A Multivariate Lagrange Inversion Formula for Asymptotic Calculations

10.37236/1371 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Edward A. Bender ◽  
L. Bruce Richmond
Keyword(s):  
Inversion Formula ◽  
Lagrange Inversion ◽  
Lagrange Inversion Formula

The determinant that is present in traditional formulations of multivariate Lagrange inversion causes difficulties when one attempts to obtain asymptotic information. We obtain an alternate formulation as a sum of terms, thereby avoiding this difficulty.

scholarly journals A ONE-PARAMETER DEFORMATION OF THE NONCOMMUTATIVE LAGRANGE INVERSION FORMULA

2011 ◽  
Vol 21 (08) ◽  
pp. 1395-1414 ◽  
Author(s):  
JEAN-PAUL BULTEL
Keyword(s):  
Hopf Algebra ◽  
Inversion Formula ◽  
Closed Formula ◽  
Lagrange Inversion ◽  
Lagrange Inversion Formula ◽  
The One ◽  
Parameter Deformation

We give a one-parameter deformation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder–Frabetti–Krattenthaler for the antipode of the noncommutative Faá di Bruno algebra. Namely, we obtain a closed formula for the antipode of the one-parameter deformation of this Hopf algebra discovered by Foissy.

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