Abstract In this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: |a32−a5| $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

中文翻译：

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类 𝓢𝓛* 的第二和第三汉克尔行列式的锐界

摘要 在本文中，我们使用了新的想法，即结合最近推导出的 Carathéodory 函数第四系数公式，代替常规三角不等式来实现 Hankel 行列式 H3(1) 和 H2(3) 的锐界：众所周知的类 𝓢𝓛* 与伯努利右双纽扣相关的星状函数。除此之外，Zalcman 泛函的锐界：|a32−a5| $\begin{array}{} |a_3^2-a_5| 𝓢𝓛* 类的 \end{array}$ 也是估计的。此外，还讨论了𝓢𝓛* 的几个有趣的结果。