%0 Journal Article %T Coefficient Bounds for a Family of Analytic Functions Linked with a Petal-Shaped Domain and Applications to Borel Distribution %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Panigrahi, Trailokya %A Murugusundaramoorthy, Gangadharan %A Pattnayak, Eureka %D 2023 %\ 04/01/2023 %V 20 %N 3 %P 33-50 %! Coefficient Bounds for a Family of Analytic Functions Linked with a Petal-Shaped Domain and Applications to Borel Distribution %K Analytic function %K Bounded turning function %K convex function %K Subordination %K Fekete-Szego functional %K Hankel determinant %K Borel distribution %R 10.22130/scma.2022.557374.1143 %X In this paper, by employing  sine hyperbolic inverse functions,  we  introduced the generalized  subfamily $\mathcal{RK}_{\sinh}(\beta)$ of analytic functions defined on the open unit disk $\Delta:=\{\xi: \xi \in \mathbb{C} \text{ and } |\xi|<1 \}$ associated with the petal-shaped domain. The bounds of the first three Taylor-Maclaurin's coefficients, Fekete-Szeg\"{o} functional and the second Hankel determinants are investigated for $f\in\mathcal{RK}_{\sinh}(\beta)$. We considered Borel distribution as an application to our main results. Consequently, a number of corollaries have been made based on our results, generalizing previous studies in this direction. %U https://scma.maragheh.ac.ir/article_704140_dcf98ffaa8c1ce1dfdb445ad63c62a58.pdf