An elliptic generalization of Schur's Pfaffian identity
Abstract
We present a Pfaffian identity involving elliptic functions, whose rational limit gives a generalization of Schur's Pfaffian identity for Pf ((xj - xi)/(xj + xi)). This identity is regarded as a Pfaffian counterpart of Frobenius identity, which is an elliptic generalization of Cauchy's determinant identity for det (1/ (xi + xj)).
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