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 \(_{q + 1} F_q (z) = \sum\limits_{n = 0}^\infty {\frac{{(a_1 ,n) \cdot \cdot \cdot (a_q ,n)(a_{q + 1} ,n)}}{{(b_1 ,n) \cdot \cdot \cdot (b_q ,n)(1,n)}}z^n ,|z|{\text{ < }}1} \)
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 aj > 0, bj > 0 so that the function \(z[_{q + 1} F_q (z)]\) is univalent in Δ. The main aim of this paper is to discuss this problem in detail for the case q = 2.
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Ponnusamy, S., Sabapathy, S. Geometric Properties of Generalized Hypergeometric Functions. The Ramanujan Journal 1, 187–210 (1997). https://doi.org/10.1023/A:1009720202474
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DOI: https://doi.org/10.1023/A:1009720202474