ISSN:
1572-9303
Keywords:
dilogarithm
;
univalent
;
close-to-convex
;
hypergeometric functions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009720202474
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