Close-to-Convexity properties of Clausen's Hypergeometric Function $_3F_2(a,b,c;d,e;z)$

New Hohlov Type Integral Operator involving Clausen's Hypergeometric Functions

We consider the integral operator $\mathcal{I}^{a,b,c}_{d,e}(f)(z)$ involving Clausen's Hypergeometric Function by means of convolution introduced by Chandrasekran and Prabhakaran for investigation. The conditions on the parameters $ a,b, c$ are determined using the integral operator $\mathcal{I}^{a,\frac{b}{2},\frac{b+1}{2}}_{\frac{c}{2}, \frac{c+1}{2}}(f)(z)$ to study the geometric properties of Clausen's Hypergeometric Function for various subclasses of univalent functions.

Clausen超几何函数$_3F_2(a,b,c;d,e;z)$的几何性质

Geometric properties of Clausen's Hypergeometric Function $_3F_2(a,b,c;d,e;z)$

克劳森的超几何函数由$${}_3F_2(a,b,c;d,e;z) = \sum_{n=0}^\infty \frac{(a)_n(b)_n(c)_n}{(d)_n(e)_n(1)_n}z^n\, ; \ a,b,c,d,e\in \mathbb{C}$$给出，条件是$d,\, e\, \neq 0,-1,-2,\cdots$在单位圆$\mathbb{D} =\{z\in \mathbb{C} \,:\, |z|<1\}$中.本文利用Hadamard积引入了一个涉及Clausen超几何函数的算子$\mathcal{I}_{a,b,c}(f)(z)$。根据泰勒系数，得到了$\mathcal{I}_{a,b,c}(f)(z)$的几何性质.

Univalent Functions with Non-Negative Coefficients involving Clausen's Hypergeometric Function

In this work, we derived the necessary and sufficient conditions on parameters for $_3F_2(^{a,b,c}_{b+1,c+1};z)$ Hypergeometric Function to be in the classes $\mathcal{M}^{\ast}(λ,α)$ and $\mathcal{N}^{\ast}(λ,α)$ and information regarding the image of function $_3F_2(^{a,b,c}_{b+1,c+1};z)$ belonging to $\mathcal{R}^τ(A,B)$ by applying the convolution operator in open unit disc $\mathbb{D} =\{z:\, |z|<1\}$.

具有单位辐角和负整参数差的Clausenian超几何函数$_3F_2$

The Clausenian hypergeometric function $_3F_2$ with unit argument and negative integral parameter differences

本文导出了具有负积分参数差的Clausenian超几何级数$_3F_2(1)$的新的显式和显式对称的三项求和公式。我们的结果概括并自然扩展了近年来许多作者发表的几个类似关系。一个适当的和有用的联系是建立在相当低估的1974年的论文P.W.卡尔森

On the order of convexity for the shifted hypergeometric functions

In the present paper, we study the order of convexity of $z\Gauss(a,b;c;z)$ with real parameters $a, b$ and $c$ where $\Gauss(a,b;c;z)$ is the Gaussian hypergeometric function. First we obtain some conditions for $z\Gauss(a,b;c;z)$ with no any finite orders of convexity by considering its asymptotic behavior around $z=1$. Then the order of convexity of $z\Gauss(a,b;c;z)$ is demonstrated for some ranges of real parameters $a,b$ and $c$. In the last section, we give some examples as the applications of the main results.

合流超几何、Lommel和Struve函数的指数星形性和凸性

Exponential starlikeness and convexity of confluent hypergeometric, Lommel and Struve functions

给出了第一类Lommel函数、第一类广义Struve函数和汇合型超几何函数的参数使这些特殊函数在单位圆盘上指数凸和指数星形的充分条件.利用微分从属的方法对结果进行了证明。还提供了一些例子来说明所获得的结果。