论文标题
一般性Rabotnov函数的部分总和
Partial sums of generalized Rabotnov function
论文作者
论文摘要
令$（\ mathbb {r} _ {α，β，γ}（z））_ {m}（z）= z+\ sum_ {n = 1}^{m} a_ {n} z^z^{n} z^{n+1} $ \ mathbb {r} _ {α，β，γ}（z）= z+\ sum_ {n = 1}^{\ infty} a_ {n} z^{n} z^{n+1} $ $ a_ {n} = n} = \ frac {n} = \ frac {β^n} n} n} n} n}^n} n}^{β{β\ eft（ \ left（γ+α\右）（n+1）\右）}}。$本文的目的是确定$ \ mathfrak {r} \ left \ left \ {\ frac {\ mathbb {r} _ {r} _ {al } {（\ Mathbb {r} _ {α，β，γ}）_ {m}（z）} \ right \}，\ mathfrak {r}％\ left \ left \ { \ frac {（\ mathbb {r} _ {α，β，γ}）_ {m}（z）}} {\ mathbb {r}％_ {α，β，β，γ}（z）（z）} \ right \}，$ $ \ mathfrak {r} \ left \ {\ frac {\ mathbb {r} _ {α，β，β，γ}（z）} {（（\ MathBb {％r} _ {α，α，α，β}） ，\ Mathfrak {r}％\ left \ {\ frac {（\ MathBb {r} _ {α，α，β，γ}）_ {m}^{\ prime}（z）}}} {z）} {％\ mathb {r}给出$ \ mathfrak {r} \ left \ {\ frac {\ mathbb {\ mathbb {i} \ left [\ mathbb {r}％_ {α，β，β} \ right]（z）} {（\ mathbb {i} \ Mathbb {r} _ {α，β，β} \ right]）_ {m}（z）} \ right \} $和$ \ mathfrak {r} \ left \ left \ left \ frac {\ frac {％（\ mathb {\ mathb {\ mathb {i} {i} \ weft [i} \ weft [\ mathbb { ）_ {m}（z）}} {％\ Mathbb {i} \ left [\ Mathbb {r} _ {α，β，β，γ} \ right]（z）} \ right \} $ $ $ \ mathbb {r} _ {α，β，γ} $的Alexander变换。还考虑了主要结果的几个示例。
Let $(\mathbb{R}_{α,β,γ}(z))_{m}(z)=z+\sum_{n=1}^{m}A_{n}z^{n+1}$ be the sequence of partial sums of the normalized Rabotnov functions $\mathbb{R}_{α,β,γ}(z)=z+\sum_{n=1}^{\infty }A_{n}z^{n+1}$ where $A_{n}=\frac{β^{n}Γ\left( γ+α\right) }{Γ\left( \left( γ+α\right) (n+1)\right) }.$ The purpose of the present paper is to determine lower bounds for $\mathfrak{R}\left \{ \frac{\mathbb{R}_{α,β,γ}(z)% }{(\mathbb{R}_{α,β,γ})_{m}(z)}\right \} ,\mathfrak{R}% \left \{ \frac{(\mathbb{R}_{α,β,γ})_{m}(z)}{\mathbb{R}% _{α,β,γ}(z)}\right \} ,$ $\mathfrak{R}\left \{ \frac{\mathbb{R}_{α,β,γ}(z)}{(\mathbb{% R}_{α,β,γ})_{m}^{\prime }(z)}\right \} ,\mathfrak{R}% \left \{ \frac{(\mathbb{R}_{α,β,γ})_{m}^{\prime }(z)}{% \mathbb{R}_{α,β,γ}(z)}\right \} .$ Furthermore, we give lower bounds for $\mathfrak{R}\left \{ \frac{\mathbb{I}\left[ \mathbb{R}% _{α,β,γ}\right] (z)}{(\mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] )_{m}(z)}\right \} $ and $\mathfrak{R}\left \{ \frac{% (\mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] )_{m}(z)}{% \mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] (z)}\right \} $ where $\mathbb{I}\left[ \mathbb{R}_{α,β,γ}\right] $ is the Alexander transform of $\mathbb{R}_{α,β,γ}$. Several examples of the main results are also considered.
