ELLIPTIC INTEGRABLE SYSTEMS Generalizations of Cauchy’s Determinant Identity and Schur’s Pfaffian Identity
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چکیده
Abstract We review several determinant and Pfaffian identities, which generalize the evaluation formulae of Cauchy’s determinant det (1/(xi + yj)) and Schur’s Pfaffian Pf ((xj − xi)/(xj + xi)). As a multi-variable generalization, we consider Cauchytype determinants and Schur-type Pfaffians of matrices with entries involving some generalized Vandermonde determinants. Also we give an elliptic generalization of Schur’s Pfaffian identity, which is a Pfaffian counterpart of Frobenius’ identity.
منابع مشابه
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تاریخ انتشار 2005