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Sufficiency for hypergeometric transforms to be associated with conic regions. (English) Zbl 1139.30308

Summary: For a certain integral operator acting on the normalized Gaussian hypergeometric function \(zF(a,b;c;z)\) given by
\[ F(a,b;c;z)=\sum^\infty_{n=0}\frac{(a,n)(b,n)}{(c,n)(1,n)}\;z^n,\quad |z|<1, \]
the author aims at finding conditions on \(a,b\) and \(c\) such that the operator maps certain subclasses of analytic functions into some other classes of functions that have nice geometric properties related to certain conic regions.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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