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{\bf Masao Ishikawa, Hiroyuki Kawamuko and Soichi Okada}
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{\bf A Pfaffian--Hafnian Analogue of Borchardt's Identity}
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We prove
$$
{\rm Pf}\! \left(
{ x_i - x_j \over (x_i + x_j)^2 }
\right)_{1 \le i, j \le 2n}
=
\prod_{1 \le i < j \le 2n}{ x_i - x_j \over x_i + x_j }
{\rm Hf}\! \left(
{ 1 \over x_i + x_j }
\right)_{1 \le i, j \le 2n}
$$
(and its variants) by using complex analysis.
This identity can be regarded as a Pfaffian--Hafnian analogue of
Borchardt's identity and as a generalization of Schur's identity.

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