A Pfaffian-Hafnian analogue of Borchardt's identity

Masao Ishikawa, Hiroyuki Kawamuko, Soichi Okada

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We prove Pf (xi - xj/(xi + x j)2)1≤i,j≤2n = π 1≤i<j≤2n 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 languageEnglish
JournalElectronic Journal of Combinatorics
Issue number1 N
Publication statusPublished - Jun 14 2005
Externally publishedYes

ASJC Scopus subject areas

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


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

Cite this