An elegant Multi-Integral that implies an even more elegant determinant identity of Dougherty and McCammond

Tewodros Amdeberhan; Doron Zeilberger

An elegant Multi-Integral that implies an even more elegant determinant identity of Dougherty and McCammond

Tewodros Amdeberhan, Doron Zeilberger

School of Arts and Sciences, Mathematics

Rutgers, The State University

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

Abstract

We state and prove an explicit evaluation of a certain multi-variate integral and use it to furnish a new, and shorter, proof of an elegant determinant identity of Michael Dougherty and Jon McCammond that came up in their study of critical values of a complex polynomial.

Original language	American English
Pages (from-to)	1-6
Number of pages	6
Journal	Palestine Journal of Mathematics
Volume	11
Issue number	4
State	Published - 2022

ASJC Scopus subject areas

Mathematics(all)

Keywords

anti-symmetric functions
Cauchy’s alternant formula
critical values
multi-integrals
Vandermonde and Jacobian matrices and determinants

Cite this

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title = "An elegant Multi-Integral that implies an even more elegant determinant identity of Dougherty and McCammond",

abstract = "We state and prove an explicit evaluation of a certain multi-variate integral and use it to furnish a new, and shorter, proof of an elegant determinant identity of Michael Dougherty and Jon McCammond that came up in their study of critical values of a complex polynomial.",

keywords = "anti-symmetric functions, Cauchy{\textquoteright}s alternant formula, critical values, multi-integrals, Vandermonde and Jacobian matrices and determinants",

author = "Tewodros Amdeberhan and Doron Zeilberger",

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language = "American English",

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AU - Zeilberger, Doron

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PY - 2022

Y1 - 2022

N2 - We state and prove an explicit evaluation of a certain multi-variate integral and use it to furnish a new, and shorter, proof of an elegant determinant identity of Michael Dougherty and Jon McCammond that came up in their study of critical values of a complex polynomial.

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KW - critical values

KW - multi-integrals

KW - Vandermonde and Jacobian matrices and determinants

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An elegant Multi-Integral that implies an even more elegant determinant identity of Dougherty and McCammond

Abstract

ASJC Scopus subject areas

Keywords

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