Certain properties for a class of analytic functions associated with hypergeometric functions (original) (raw)

Subclasses of analytic functions associated with the generalized hypergeometric function

Computers & Mathematics with Applications, 2009

Using the generalized hypergeometric function, we study a class Φ p k (q, s; A, B, λ) of analytic functions with negative coefficients. Coefficient estimates, distortion theorem, extreme points and the radii of close-to-convexity and convexity for this class are given. We also derive many results for the modified Hadamard product of functions belonging to the class Φ p k (q, s; A, B, λ).

INCLUSION RELATIONS BETWEEN CLASSES OF HYPERGEOMETRIC FUNCTIONS

ABSTILCT The use of hypergeometric functions in univalent function theory received special attention after the surprising application of such functions by de Branges in the proof of the 70-year old Bieberbach Conjecture. In this paper we consider certain classes of analytic functions and examine the distortion and containment properties of generalized hypergeometric hnctions under some operators in these classes.

A Subclass of Analytic Functions Associated with Hypergeometric Functions

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

Classes of analytic functions associated with the generalized hypergeometric function

Applied Mathematics and Computation, 1999

Using the generalized hypergeometric function, we introduce and study a class of analytic functions with negative coecients. Coecients estimates, distortion theorems, extreme points, and the radii of convexity and starlikeness for this class are given. Relevant connections of these results with those in several earlier investigations are indicated. Ó . 0096-3003/99/$ ± see front matter Ó 1999 Elsevier Science Inc. All rights reserved. PII: S 0 0 9 6 -3 0 0 3 ( 9 8 ) 1 0 0 4 2 -5

On Properties of Hypergeometric-Type Functions

2006

ALVAREZ-NODARSE Abstract. The functions of hypergeometric type are the solutions y = y (z) of the dierential equation (z)y00 + (z)y0 + y = 0, where and are poly- nomials of degrees not higher than 2 and 1, respectively, and is a constant. Here we consider a class of functions of hypergeometric type: those that sat- isfy the condition +

Certain New Subclasses of Analytic Functions Involving Generalized Hypergeometric Function

Journal of the Nigerian Mathematical Society, 2019

In this work the author considered new subclasses of analytic univalent functions using certain linear operator. With the operator, the author was able to study several new and existing subclasses of analytic univalent functions in the unit disk. The results presented in this paper include, coefficient estimates (which were later used to investigate certain subclasses of analytic functions with fixed finitely many coefficients) and distortion theorems for functions belonging to these subclasses. Furthermore, some relationships between these subclasses were also discussed.

Some properties of the hypergeometric functions of one variable

2011

In this paper we introduced the novel concept of basic hypergeometric series and the hypergeometric function. We express many of common mathematical function in terms of the hypergeometric function. Gauss’ contigous relations, some integral formulas, Recurrence relations, transformation formulas, values at the special points.

Further results on generalized hypergeometric functions

Applied Mathematics and Computation, 2003

Recently, Virchenko et al. [Integral Transform. and Spec. Funct. 12 (1) (2001) 89-100] have defined and studied a generalized hypergeometric function of the form 2 R s 1 ða; b; c; s; zÞ ¼ CðcÞ CðbÞCðc À bÞ Z 1 0 t bÀ1 ð1 À tÞ cÀbÀ1 ð1 À zt s Þ dt: