Keywords: Srivastava-Daoust function, matrix arguments, matrix transform. In this paper I have defined the Srivastava and Daoust multiple hypergeometric function of matrix arguments and have established an integral representation for it using the Mathai’s matrix tansform technique. 1.

Abstract: We investigate analytic solutions to Wu’s equations and their symmetry property, singularities and monodromy, relating them to quasi hypergeometric functions. We finally give the monodromy theorem for them in one, two and arbitrary dimensional cases (see Theorem 1, 2 and 3). 1. Quasi-Hypergeometric Functions Associated with Wu’s Equations Let β ′ = (β ′ i,j)n i,j=1 be an n × n matrix with real entries β ′ i,j. Being given a point z = (z1,...,zn) ∈ Cn, Wu’s equations with respect to w1,...,wn are described as wi − 1 = ziw β ′ 1i 1 ···w β ′ ni n, (1.1) 1 ≤ i ≤ n. Wu’s equations have appeared as fundamental equations determining mutually fractional exclusion statistics in statistical mechanics (see [25].) By applying the multivariable Lagrange inversion formula, the second author has shown that the unique holomorphic solution to (1.1) can be explicitly expressed as a special type of quasi hypergeometric functions (see [15]). It is important to study the singularity of this solution both in mathematics and in theoretical physics, because it gives a global nature of the function and also is related to critical phenomena in statistical physics. However we do not discuss any physical aspect. The purpose of this note is to give a monodromy formula for the solutions w(z) to (1.1). Under a certain non-degenerate condition, we first give 3n kinds of the local solutions to (1.1) near the points w = (w1,...,wn) such that wj = 0, 1, ∞ in the compactified space (CP 1) n.476 K. Aomoto, K. Iguchi To do that, we consider the n dimensional real variety in the complex affine space C n,