Hypergeometric Functions in Sequential Analysis

Hypergeometric Functions

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.

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometr...

Hypergeometric functions in one variable

This is a Fuchsian equation of order n with singularities at 0, 1,∞. The local exponents read, 1− β1, . . . , 1− βn at z = 0 α1, . . . , αn at z =∞ 0, 1, . . . , n− 2, −1 + ∑n 1 (βi − αi) at z = 1 When the βi are distinct modulo 1 a basis of solutions at z = 0 is given by the functions z1−βi nFn−1 ( α1 − βi + 1, . . . , αn − βi + 1 β1 − βi + 1, ..∨.., βn − βi + 1 ∣∣∣∣ z) (i = 1, . . . , n). Her...