Abstract In this present investigation, we will concern with the family of normalized analytic error function which is defined by Erf(z)=πz2erf(z)=z+∑n=2∞(−1)n−1(2n−1)(n−1)!zn. $$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$ By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

中文翻译：

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赋予三角多项式的 q-starlike 和 q-convex 误差函数的扩展

摘要 在本研究中，我们将关注归一化解析误差函数族，其定义为 Erf(z)=πz2erf(z)=z+∑n=2∞(−1)n−1(2n−1)( n−1)!zn。$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\ overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n} . \end{array}$$ 通过使用三角多项式 Un(p, q, eiθ) 以及从属规则，我们引入了几个由 𝔮-starlike 和 𝔮-convex 误差函数组成的新类。之后，我们推导出这些类中函数的一些系数不等式。