Geometric Properties of Generalized Hypergeometric Functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Geometric Properties of Generalized Hypergeometric Functions

Authors:	Ponnusamy S. Sabapathy S.

Affiliation:	(1) Department of Mathematics, Indian Institute of Technology, Guwahati-, 781 001 Assam, India;(2) Department of Mathematics, A.A. Government Arts College, Musiri-, 621 201 Tamilnadu, India

Abstract:	Let $_{q + 1} F_q (z): = _{q + 1} F_q (a_1 ,a_2 ,...,a_{q + 1} ;b_1 ,...,b_q ;z)$ denote the generalized hypergeometric function $_{q + 1} F_q (z) = sumlimits_{n = 0}^infty {frac{{(a_1 ,n) cdot cdot cdot (a_q ,n)(a_{q + 1} ,n)}}{{(b_1 ,n) cdot cdot cdot (b_q ,n)(1,n)}}z^n ,\|z\|{text{ < }}1}$ where no denominator parameter can be zero or a negative integer and (a,n) denotes the ascending factorial notation. Ponnusamy and Vuorinen raised the problem of finding conditions on the parameters a_j > 0, b_j > 0 so that the function $z[_{q + 1} F_q (z)]$ is univalent in . The main aim of this paper is to discuss this problem in detail for the case q = 2.

Keywords:	dilogarithm univalent close-to-convex hypergeometric functions
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