### 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 | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Arithmetic mean
- Geometric mean
- Hurwitz' identity
- Muirhead's identity

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Journal of Mathematical Analysis*,

*8*(29-32), 1525-1542. https://doi.org/10.12988/ijma.2014.46170

**Identities for the difference between the arithmetic and geometric means.** / Fujiwara, Kazumasa; Ozawa, Tohru.

Research output: Contribution to journal › Article

*International Journal of Mathematical Analysis*, vol. 8, no. 29-32, pp. 1525-1542. https://doi.org/10.12988/ijma.2014.46170

}

TY - JOUR

T1 - Identities for the difference between the arithmetic and geometric means

AU - Fujiwara, Kazumasa

AU - Ozawa, Tohru

PY - 2014

Y1 - 2014

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.

KW - Arithmetic mean

KW - Geometric mean

KW - Hurwitz' identity

KW - Muirhead's identity

UR - http://www.scopus.com/inward/record.url?scp=84908235447&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908235447&partnerID=8YFLogxK

U2 - 10.12988/ijma.2014.46170

DO - 10.12988/ijma.2014.46170

M3 - Article

VL - 8

SP - 1525

EP - 1542

JO - International Journal of Mathematical Analysis

JF - International Journal of Mathematical Analysis

SN - 1312-8876

IS - 29-32

ER -