scholarly journals On Certain Subclass of Meromorphic Spirallike Functions Involving the Hypergeometric Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Shi ◽  
Zhi-Gang Wang
Keyword(s):  
Hypergeometric Function ◽  
Integral Representations ◽  
Coefficient Estimates ◽  
Spirallike Functions ◽  
Convolution Properties

We introduce and investigate a new subclassMm1(θ,λ,η)of meromorphic spirallike functions. Such results as integral representations, convolution properties, and coefficient estimates are proved. The results presented here would provide extensions of those given in earlier works. Several other results are also obtained.

scholarly journals On Some Classes of Spirallike Functions Defined by the Salagean Operator

2019 ◽  
Author(s):  
Mohammad Mehdi Shabani ◽  
Saeed Hashemi Sababe
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Coefficient Estimates ◽  
Inclusion Properties ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Spirallike Functions ◽  
Convolution Properties ◽  
Necessary And Sufficient

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator

2019 ◽  
Vol 26 (3) ◽  
pp. 449-458
Author(s):  
Khalida Inayat Noor ◽  
Rashid Murtaza ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Integral Operators ◽  
Generalized Hypergeometric Functions ◽  
Convolution Properties ◽  
Appl Math ◽  
Inclusion Results

Abstract In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in {|z|<1} , by using the hypergeometric function and the Owa–Srivastava operator {\Omega^{\alpha}} defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

scholarly journals The monodromy representation and twisted period relations for Appell’s hypergeometric function F 4

2015 ◽  
Vol 217 ◽  
pp. 61-94
Author(s):  
Yoshiaki Goto ◽  
Keiji Matsumoto
Keyword(s):  
Differential Equations ◽  
Hypergeometric Function ◽  
Hypergeometric Series ◽  
Integral Representations ◽  
Monodromy Representation ◽  
Homology Groups ◽  
Linearly Independent ◽  
Fundamental Systems

AbstractWe consider the systemF4(a, b, c)of differential equations annihilating Appell's hypergeometric seriesF4(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric seriesF4. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation ofF4(a, b, c)and the twisted period relations for the fundamental systems of solutions ofF4.

scholarly journals Integral representations of generalized Lauricella hypergeometric functions

1992 ◽  
Vol 15 (4) ◽  
pp. 653-657 ◽  
Author(s):  
Vu Kim Tuan ◽  
R. G. Buschman
Keyword(s):  
Integral Representation ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Appell Function

The generalized hypergeometric function was introduced by Srivastava and Daoust. In the present paper a new integral representation is derived. Similarly new integral representations of Lauricella and Appell function are obtained.

scholarly journals Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 48
Author(s):  
Kottakkaran Sooppy Nisar
Keyword(s):  
Zeta Function ◽  
Hypergeometric Function ◽  
Summation Formula ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized hypergeometric function. To strengthen the main results we also consider some important special cases.

A Class of Generalized Hypergeometric Functions in Several Variables

1992 ◽  
Vol 44 (6) ◽  
pp. 1317-1338 ◽  
Author(s):  
Zhimin Yan
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Hypergeometric Function ◽  
Unique Solution ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Gaussian Hypergeometric Function ◽  
Generalized Hypergeometric Functions ◽  
Several Variables

AbstractWe study a class of generalized hypergeometric functions in several variables introduced by A. Korânyi. It is shown that the generalized Gaussian hypergeometric function is the unique solution of a system partial differential equations. Analogues of some classical results such as Kummer relations and Euler integral representations are established. Asymptotic behavior of generalized hypergeometric functions is obtained which includes some known estimates.

scholarly journals Convolution Properties for Some Subclasses of Meromorphic Functions of Complex Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa ◽  
H. M. Zayed
Keyword(s):  
Unit Disc ◽  
Meromorphic Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Convolution Properties

Making use of the operatorLυfor functions of the formfz=1/z+∑k=1∞akzk-1, which are analytic in the punctured unit discU∗={z:z∈Cand0<|z|<1}=U∖{0}, we introduce two subclasses of meromorphic functions and investigate convolution properties, coefficient estimates, and containment properties for these subclasses.

scholarly journals On Certain Subclasses of Meromorphic Functions with Positive and Fixed Second Coefficients Involving the Liu-Srivastava Linear Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
N. Magesh ◽  
N. B. Gatti ◽  
S. Mayilvaganan
Keyword(s):  
Linear Operator ◽  
Linear Combination ◽  
Hypergeometric Function ◽  
Meromorphic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Generalized Hypergeometric Function ◽  
Coefficient Estimates ◽  
Convex Linear Combination ◽  
Meromorphic Univalent Functions

We introduce and study a subclass ΣP(γ,k,λ,c) of meromorphic univalent functions defined by certain linear operator involving the generalized hypergeometric function. We obtain coefficient estimates, extreme points, growth and distortion inequalities, radii of meromorphic starlikeness, and convexity for the class ΣP(γ,k,λ,c) by fixing the second coefficient. Further, it is shown that the class ΣP(γ,k,λ) is closed under convex linear combination.

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