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Investigates constraints on parameters affecting close-to-convexity in inverse hypergeometric functions, suggesting new insights into function classes.
The normalized inverse hypergeometric function zFν−1(d, e, f; z) = ∑s=0∞ Aszs+1 is considered, where As = (f)s(ν + 1)s / (d)s(e)s. We aim to provide constraints on d, e, f, and ν under which zFν−1(d, e, f; z) belongs to various subclasses of the class of close-to-convex functions. Coefficient characterizations of these families are derived under additional conditions. Some associated operators are also discussed.
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Hussain et al. (2026) studied this question.
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