scholarly journals Euler and Laplace integral representations of GKZ hypergeometric functions I

2020 ◽  
Vol 96 (9) ◽  
pp. 75-78
Author(s):  
Saiei-Jaeyeong Matsubara-Heo
Keyword(s):  
Hypergeometric Functions ◽  
Integral Representations ◽  
Laplace Integral

scholarly journals Generating Functions for Some Hypergeometric Functions of Four Variables via Laplace Integral Representations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Jihad Younis ◽  
Maged Bin-Saad ◽  
Ashish Verma
Keyword(s):  
Generating Functions ◽  
Hypergeometric Functions ◽  
Essential Role ◽  
Integral Representations ◽  
Laplace Integral ◽  
Special Cases ◽  
Generating Relations

Generating functions plays an essential role in the investigation of several useful properties of the sequences which they generate. In this paper, we establish certain generating relations, involving some quadruple hypergeometric functions introduced by Bin-Saad and Younis. Some interesting special cases of our main results are also considered.

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.

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.

Multi-parametric mittag-leffler functions and their extension

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Anatoly Kilbas ◽  
Anna Koroleva ◽  
Sergei Rogosin
Keyword(s):  
Fractional Calculus ◽  
Historical Development ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Integral Representations ◽  
Generalized Hypergeometric Functions ◽  
Late Professor ◽  
Wright Generalized Hypergeometric Functions

AbstractThis paper surveys one of the last contributions by the late Professor Anatoly Kilbas (1948–2010) and research made under his advisorship. We briefly describe the historical development of the theory of the discussed multi-parametric Mittag-Leffler functions as a class of the Wright generalized hypergeometric functions. The method of the Mellin-Barnes integral representations allows us to extend the considered functions to the case of arbitrary values of parameters. Thus, the extended Mittag-Leffler-type functions appear. The properties of these special functions and their relations to the fractional calculus are considered. Our results are based mainly on the properties of the Fox H-functions, as one of the widest class of special functions.

scholarly journals Certain Integrals Associated with Hypergeometric Functions of Four Variables

2019 ◽  
pp. 325-341
Author(s):  
Maged G. Bin-Saad ◽  
Jihad A. Younis
Keyword(s):  
Hypergeometric Functions ◽  
Hypergeometric Series ◽  
Integral Representations ◽  
Laplace Type

The main objective of this paper is to present integral representations of Euler type and Laplace type for five new hypergeometric series of four variables.

scholarly journals On A Logarithmic Mittag-Leffler Function, its Properties and Applications

2021 ◽  
Author(s):  
M.A. Pathan ◽  
Hemant Kumar
Keyword(s):  
Infectious Diseases ◽  
Hypergeometric Functions ◽  
Point Of View ◽  
Integral Representations ◽  
Contour Integral ◽  
Application Point

In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions. 

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