Hypergeometric functions and conformal mapping

Mapping Properties for Convolutions Involving Hypergeometric Functions

For μ ≥ 0, we consider a linear operator Lμ : A → A defined by the convolution fμ∗f , where fμ = (1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))′. Let φ∗(A,B) denote the class of normalized functions f which are analytic in the open unit disk and satisfy the condition zf ′/f ≺ (1+Az)/1+Bz, −1 ≤ A < B ≤ 1, and let Rη(β) denote the class of normalized analytic functions f for which there exits a number η∈ (...

Mapping Properties of Basic Hypergeometric Functions

It is known that the ratio of Gaussian hypergeometric functions can be represented by means of g -fractions. In this work, the ratio of q -hypergeometric functions are represented by means of g -fractions that lead to certain results on q -starlikeness of the q -hypergeometric functions defined on the open unit disk. Corresponding results for the q -convex case are also obtained.

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.

Binary Forms, Hypergeometric Functions and the Schwarz-christoffel Mapping Formula

In a previous paper, it was shown that HE is a binary form with complex coefficients having degree n > 3 and discriminant Df ^ 0, and if Af is the area of the region \F(x, y)\ < 1 in the real affine plane, then \DF\llni-"-^AF < 1B{\, \), where B{\ , 1) denotes the Beta function with arguments of 1/3 . This inequality was derived by demonstrating that the sequence {M„} defined by Mn = max|Df \Ui...

Hypergeometric Functions