A Pfaffian-Hafnian analogue of Borchardt's identity

Masao Ishikawa; Hiroyuki Kawamuko; Soichi Okada

A Pfaffian-Hafnian analogue of Borchardt's identity

Masao Ishikawa, Hiroyuki Kawamuko, Soichi Okada

Research output: Contribution to journal › Article

Abstract

We prove Pf (x_i - x_j/(x_i + x _j)²)_1≤i,j≤2n = π _1≤i<j≤2n x_i - _j/x_i + _j · Hf (1/x_i + x_j) _1≤i,j≤2n (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity.

Original language	English
Journal	Electronic Journal of Combinatorics
Volume	12
Issue number	1 N
Publication status	Published - Jun 14 2005
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

Access to Document

Fingerprint Dive into the research topics of 'A Pfaffian-Hafnian analogue of Borchardt's identity'. Together they form a unique fingerprint.

Cite this

Ishikawa, M., Kawamuko, H., & Okada, S. (2005). A Pfaffian-Hafnian analogue of Borchardt's identity. Electronic Journal of Combinatorics, 12(1 N).

@article{9aedf49788d84b159c81bf571316f1e3,

title = "A Pfaffian-Hafnian analogue of Borchardt's identity",

abstract = "We prove Pf (xi - xj/(xi + x j)2)1≤i,j≤2n = π 1≤i xi - j/xi + j · Hf (1/xi + xj) 1≤i,j≤2n (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity.",

author = "Masao Ishikawa and Hiroyuki Kawamuko and Soichi Okada",

year = "2005",

month = jun,

day = "14",

language = "English",

volume = "12",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1 N",

}

TY - JOUR

T1 - A Pfaffian-Hafnian analogue of Borchardt's identity

AU - Ishikawa, Masao

AU - Kawamuko, Hiroyuki

AU - Okada, Soichi

PY - 2005/6/14

Y1 - 2005/6/14

N2 - We prove Pf (xi - xj/(xi + x j)2)1≤i,j≤2n = π 1≤i xi - j/xi + j · Hf (1/xi + xj) 1≤i,j≤2n (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity.

AB - We prove Pf (xi - xj/(xi + x j)2)1≤i,j≤2n = π 1≤i xi - j/xi + j · Hf (1/xi + xj) 1≤i,j≤2n (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian-Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity.

UR - http://www.scopus.com/inward/record.url?scp=21244456491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21244456491&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21244456491

VL - 12

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1 N

ER -