scholarly journals ON A NEW CLASS OF LAPLACE-TYPE DOUBLE INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS

2021 ◽  
Vol 133 (2) ◽  
pp. 89-100
Author(s):  
Shoukat Ali ◽  
Radha Mathur
Keyword(s):  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Laplace Type ◽  
Double Integrals

scholarly journals On a New Class of Laplace-Type Integrals Involving Generalized Hypergeometric Functions

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 87 ◽  
Author(s):  
Wolfram Koepf ◽  
Insuk Kim ◽  
Arjun K. Rathie
Keyword(s):  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Special Cases ◽  
Laplace Type

In the theory of generalized hypergeometric functions, classical summation theorems for the series 2 F 1 , 3 F 2 , 4 F 3 , 5 F 4 and 7 F 6 play a key role. Very recently, Masjed-Jamei and Koepf established generalizations of the above-mentioned summation theorems. Inspired by their work, the main objective of the paper is to provide a new class of Laplace-type integrals involving generalized hypergeometric functions p F p for p = 2 , 3 , 4 , 5 and 7 in the most general forms. Several new and known cases have also been obtained as special cases of our main findings.

scholarly journals Subclass of Multivalent Harmonic Functions Defi…ned by Wright Generalized Hypergeometric Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
M. K. Aouf ◽  
A. O. Moustafa ◽  
E. A. Adwan
Keyword(s):  
Harmonic Functions ◽  
Hypergeometric Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Function Coefficient ◽  
Distortion Bounds ◽  
Wright Generalized Hypergeometric Functions

We introduce a new class of multivalent harmonic functions defi…ned by Wright generalized hypergeometric function. Coefficient estimates, extreme points, distortion bounds, and convex combination for functions belonging to this class are obtained.

scholarly journals A Study of Extensions of Classical Summation Theorems for the Series $$_{3}F_{2}$$ and $$_{4}F_{3}$$ with Applications

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Mohamed M. Awad ◽  
Wolfram Koepf ◽  
Asmaa O. Mohammed ◽  
Medhat A. Rakha ◽  
Arjun K. Rathie
Keyword(s):  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Special Cases ◽  
Laplace Type

AbstractVery recently, Masjed-Jamei & Koepf [Some summation theorems for generalized hypergeometric functions, Axioms, 2018, 7, 38, 10.3390/axioms 7020038] established some summation theorems for the generalized hypergeometric functions. The aim of this paper is to establish extensions of some of their summation theorems in the most general form. As an application, several Eulerian-type and Laplace-type integrals have also been given. Results earlier obtained by Jun et al. and Koepf et al. follow special cases of our main findings.

scholarly journals EVALUATION OF A NEW CLASS OF EULERIAN'S TYPE INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTIONS

2019 ◽  
pp. 855
Author(s):  
Insuk Kim ◽  
Gradimir V. Milovanović ◽  
Arjun Rathie
Keyword(s):  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Special Cases

Very recently Masjed-Jamei and Koepf [Axioms 2018, 7 (2), 38] established interesting and useful generalizations of various classical summation theorems for the${}_{2}F_{1}$, ${}_{3}F_{2}$, ${}_{4}F_{3}$, ${}_{5}F_{4}$ and ${}_{6}F_{5}$ generalized hypergeometric series.The main aim of this paper is to establish eleven Eulerian's type integrals involving generalized hypergeometric functions by employing these theorems. Several special cases (known and unknown) have also been given.

scholarly journals A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Firas Ghanim ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
The Other ◽  
Radius Of Starlikeness ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Coefficient Bound ◽  
Characterization Property

We introduce a new subclass of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution). A characterization property such as the coefficient bound is obtained for this class. The other related properties, which are investigated in this paper, include the distortion and the radius of starlikeness. We also consider several applications of our main results to the generalized hypergeometric functions.

scholarly journals A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
F. Ghanim ◽  
M. Darus
Keyword(s):  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
The Other ◽  
Generalized Hypergeometric Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Characterization Property ◽  
Class Of Functions

We introduce a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically functions related to Cho-Kwon-Srivastava operator. A characterization property giving the coefficient bounds is obtained for this class of functions. The other related properties, which are investigated in this paper, include distortion and the radii of starlikeness and convexity. We also consider several applications of our main results to generalized hypergeometric functions.

Sign in / Sign up

Export Citation Format

Share Document