The Determinant of a Hypergeometric Period Matrix and a Generalization of Selberg’s Integral
نویسندگان
چکیده
In an earlier paper (Adv. Appl. Math. 29 (2002), 137–151) on the determinants of certain period matrices, we formulated a conjecture about the determinant of a certain hypergeometric matrix. In this article, we establish this conjecture by constructing a system of linear equations in which that determinant is one of the variables. As a consequence, we obtain the value of an integral which generalizes the well-known multidimensional beta integral of A. Selberg (Norsk. Mat. Tidsskr. 26, 71–78) and some hypergeometric determinant formulas of A. Varchenko (Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), 1206–1235; 54 (1990), 146–158).
منابع مشابه
Generalization of Dodgson's "Virtual Center" Method; an Efficient Method for Determinant Calculation
Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the Dodgson method's structure and provides a solution for the problemof "dividing by zero" called "virtua...
متن کاملIntegral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant
Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
متن کاملApplication of some integral transforms and multiple hypergeometric functions in modeling randomly weighted average of some random variables
This article has no abstract.
متن کاملLommel Matrix Functions
The main objective of this work is to develop a pair of Lommel matrix functions suggested by the hypergeometric matrix functions and some of their properties are studied. Some properties of the hypergeometric and Bessel matrix functions are obtained.
متن کاملSome Relations on Laguerre Matrix Polynomials
The main object of this paper is to give a di erent approach to proof of generating matrix functions for Laguerre matrix polynomials. We also obtain the hypergeometric matrix representations, addition theorem, nite summation formula and an integral representation for Laguerre matrix polynomials. We get the relations between Laguerre, Legendre and Hermite matrix polynomials. We get the generatin...
متن کامل