On partial sums of four parametric Wright function
Commun. Korean Math. Soc. 2022 Vol. 37, No. 3, 681-692
https://doi.org/10.4134/CKMS.c200469
Published online July 5, 2022
Printed July 31, 2022
Muhey U Din
Government Post Graduate Islamia College Faisalabad
Abstract : Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al.~\cite{din}. Some examples are also discussed for the sake of better understanding of this article.
Keywords : Partial sums, analytic functions, normalized four parametric Wright function
MSC numbers : Primary 30C45, 33C10; Secondary 30C20, 30C75
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