The Euler beta-function, the Vandermonde determinant, the Legendre equation and critical values of linear functions on a configuration of hyperplanes. II. (Russian) Zbl 0699.33004

Varchenko, A. N.

Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 1, 146-158 (1990).

This is a continuation of the part I by the same author [see ibid. 53, No.6, 1206-1235 (1989; Zbl 0695.33004)] concerning the construction of generalized Beta function associated with a configuration of hyperplanes in an affine space. This part contains proofs of the main theorems and also a conjecture on a formula for the case of singular configuration.

Reviewer: A.Kaneko

MSC:

33C60	Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
33B15	Gamma, beta and polygamma functions

Keywords:

hypergeometric integral; period matrix; generalized Beta function