Identities for the difference between the arithmetic and geometric means

Kazumasa Fujiwara; Tohru Ozawa

doi:10.12988/ijma.2014.46170

Identities for the difference between the arithmetic and geometric means

Kazumasa Fujiwara, Tohru Ozawa

School of Advanced Science and Engineering

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

1 Citation (Scopus)

Abstract

We prove a formula which expresses the difference between the arithmetic mean of variables of odd numbers and the corresponding geometric mean in the form of a linear combination of independent variables with coefficients given by sums of squares of polynomials.

Original language	English
Pages (from-to)	1525-1542
Number of pages	18
Journal	International Journal of Mathematical Analysis
Volume	8
Issue number	29-32
DOIs	https://doi.org/10.12988/ijma.2014.46170
Publication status	Published - 2014

Keywords

Arithmetic mean
Geometric mean
Hurwitz' identity
Muirhead's identity

ASJC Scopus subject areas

Mathematics(all)

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10.12988/ijma.2014.46170

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title = "Identities for the difference between the arithmetic and geometric means",

abstract = "We prove a formula which expresses the difference between the arithmetic mean of variables of odd numbers and the corresponding geometric mean in the form of a linear combination of independent variables with coefficients given by sums of squares of polynomials.",

keywords = "Arithmetic mean, Geometric mean, Hurwitz' identity, Muirhead's identity",

author = "Kazumasa Fujiwara and Tohru Ozawa",

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year = "2014",

doi = "10.12988/ijma.2014.46170",

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AU - Fujiwara, Kazumasa

AU - Ozawa, Tohru

PY - 2014

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N2 - We prove a formula which expresses the difference between the arithmetic mean of variables of odd numbers and the corresponding geometric mean in the form of a linear combination of independent variables with coefficients given by sums of squares of polynomials.

AB - We prove a formula which expresses the difference between the arithmetic mean of variables of odd numbers and the corresponding geometric mean in the form of a linear combination of independent variables with coefficients given by sums of squares of polynomials.

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KW - Geometric mean

KW - Hurwitz' identity

KW - Muirhead's identity

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JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

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ER -

Identities for the difference between the arithmetic and geometric means

Abstract

Keywords

ASJC Scopus subject areas

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