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.
| Original language | English |
|---|---|
| Journal | Electronic Journal of Combinatorics |
| Volume | 12 |
| Issue number | 1 N |
| Publication status | Published - Jun 14 2005 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
Cite this
A Pfaffian-Hafnian analogue of Borchardt's identity. / Ishikawa, Masao; Kawamuko, Hiroyuki; Okada, Soichi.
In: Electronic Journal of Combinatorics, Vol. 12, No. 1 N, 14.06.2005.Research output: Contribution to journal › Article
}
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 -