{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T03:41:02Z","timestamp":1784346062942,"version":"3.55.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove $$ {\\rm Pf}\\! \\left( { x_i - x_j \\over (x_i + x_j)^2 } \\right)_{1 \\le i, j \\le 2n} = \\prod_{1 \\le i  &lt;  j \\le 2n}{ x_i - x_j \\over x_i + x_j } {\\rm Hf}\\! \\left( { 1 \\over x_i + x_j } \\right)_{1 \\le i, j \\le 2n} $$ (and its variants) by using complex analysis. This identity can be regarded as a Pfaffian\u2013Hafnian analogue of Borchardt's identity and as a generalization of Schur's identity.<\/jats:p>","DOI":"10.37236\/1976","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:36Z","timestamp":1578719496000},"source":"Crossref","is-referenced-by-count":14,"title":["A Pfaffian&amp;ndash;Hafnian Analogue of Borchardt's Identity"],"prefix":"10.37236","volume":"12","author":[{"given":"Masao","family":"Ishikawa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hiroyuki","family":"Kawamuko","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Soichi","family":"Okada","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2005,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:49:24Z","timestamp":1579322964000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1n9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1976","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6,14]]},"article-number":"N9"}}