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arxiv: math/0412038 · v1 · submitted 2004-12-02 · 🧮 math.CA · math.CO

An elliptic generalization of Schur's Pfaffian identity

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

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