Geodesic
The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a~configuration of hyperplanes.~I
Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 543-571

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When working with a set of linear functions and the configration of hyperplanes they define, one encounters a matrix of multidimensional hypergeometric integrals. We give a formula which expresses the determinant of this matrix in terms of critical values of the linear functions restricted to the configuration. Bibliography: 26 titles. 
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A. N. Varchenko. The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a~configuration of hyperplanes.~I. Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 543-571. http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a2/