正规化Dini函数的部分和
Partial sums of the normalized Dini functions
摘要：
令$\left( w_{α,v}\right) _{m}(z)=z+\sum\limits_{n=1}^{m}a_{n}z^{n+1} $是归一化Dini函数$w_{α,v}(z)=z+\sum\limits_{n=1}^{\infty }a_{n}z^{n+1}$的部分和的序列，其中$a_{n}=\frac{\left( -1\right) ^{n}\left( 2n+α\right) }{α4^{n}n!\left( v+1\right) _{n}% }$。本文的目的是获得$\mathcal{R} \left\{ \frac{w_{α,v}(z)}{\left( w_{α,v}\right) _{m}(z)}\right\} ,$、$\mathcal{R}\left\{ \frac{\left( w_{α,v}\right) _{m}(z)}{w_{α,v}(z)}\right\} ,$、$\mathcal{R}\left\{ \frac{w_{α,v}^{^{\prime }}(z)}{ \left( w_{α,v}\right) _{m}^{^{\prime }}(z)}\right\}$和$\mathcal{R} \left\{ \frac{\left( w_{α,v}\right) _{m}^{^{\prime }}(z)}{w_{α,v}^{^{\prime }}(z)}\right\}$的下界。并给出了一些函数象域的几何描述。
英文摘要：
Let $\left( w_{α,v}\right) _{m}(z)=z+\sum\limits_{n=1}^{m}a_{n}z^{n+1} $ be the sequence of partial sums of normalized Dini functions $w_{α,v}(z)=z+\sum\limits_{n=1}^{\infty }a_{n}z^{n+1}$ where $a_{n}=\frac{\left( -1\right) ^{n}\left( 2n+α\right) }{α4^{n}n!\left( v+1\right) _{n}% }$. The aim of the present paper is to obtain lower bounds for $\mathcal{R} \left\{ \frac{w_{α,v}(z)}{\left( w_{α,v}\right) _{m}(z)}\right\} ,$ $\mathcal{R}\left\{ \frac{\left( w_{α,v}\right) _{m}(z)}{w_{α,v}(z)}\right\} ,$ $\mathcal{R}\left\{ \frac{w_{α,v}^{^{\prime }}(z)}{ \left( w_{α,v}\right) _{m}^{^{\prime }}(z)}\right\}$ and $\mathcal{R} \left\{ \frac{\left( w_{α,v}\right) _{m}^{^{\prime }}(z)}{w_{α,v}^{^{\prime }}(z)}\right\}$ . Also we give a few geometric description regarding image domains of some functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
