ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS

Shaul Zemel

doi:10.61091/ojac-1806

ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS

Shaul Zemel^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves fewer products of building blocks of multinomial type, and we study the combinatorics of the coefficients showing up in both formulae.

Original language	English
Article number	06
Journal	Online Journal of Analytic Combinatorics
Issue number	18
DOIs	https://doi.org/10.61091/ojac-1806
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Combinatorial Press. All rights reserved.

Keywords

Combinatorial Coefficients
Higher Partial Derivatives
Implicit Functions

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10.61091/ojac-1806

Cite this

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abstract = "We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves fewer products of building blocks of multinomial type, and we study the combinatorics of the coefficients showing up in both formulae.",

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ON HIGHER PARTIAL DERIVATIVES OF IMPLICIT FUNCTIONS AND THEIR COMBINATORICS

Abstract

Bibliographical note

Keywords

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