Hypergeometric functions on complex matrix space

Three Lectures on Hypergeometric Functions

In this course we will study multivariate hypergeometric functions in the sense of Gel’fand, Kapranov, and Zelevinsky (GKZ systems). These functions generalize the classical hypergeometric functions of Gauss, Horn, Appell, and Lauricella. We will emphasize the algebraic methods of Saito, Sturmfels, and Takayama to construct hypergeometric series and the connection with deformation techniques in...

Notes on A-hypergeometric Functions

Hypergeometric Functions

Subclasses of analytic functions associated with Fox-Wright’s generalized hypergeometric functions based on Hilbert space operator

In this paper, we define a generalized class of starlike functions which are based upon some convolution operators on Hilbert space involving the Fox-Wright generalization of the classical hypergeometric pFq function (with p numerator and q denominator parameters). The various results presented in this paper include (for example) normed coefficient inequalities and estimates, distortion theorem...

Integral 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.