scholarly journals Some inequalities involving two generalized beta functions in n variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mustapha Raïssouli ◽  
Salma I. El-Soubhy
Keyword(s):  
Gamma Function ◽  
Generalized Functions ◽  
Gamma Functions ◽  
Generalized Gamma ◽  
Several Variables ◽  
Generalized Gamma Function ◽  
Generalized Beta Functions

AbstractThe beta and gamma functions have recently seen several developments and various extensions because of their nice properties and interesting applications. The contribution of this paper falls within this framework. After introducing a generalized gamma function and two generalized beta functions in several variables, we investigate some inequalities involving these generalized functions.

scholarly journals A note on a functional equation

1973 ◽  
Vol 15 (4) ◽  
pp. 385-388
Author(s):  
Chung-Ming An
Keyword(s):  
Functional Equation ◽  
Dirichlet Series ◽  
Gamma Function ◽  
Generalized Gamma ◽  
Special Cases ◽  
Generalized Gamma Function

The object of this note is to give an aspect to the problem of the functional equation of the generalized gamma function and Dirichlet series which are defined in [1]. In general, we cannot answer the problem yet. But it is worthy to attack this problem for some special cases.

p-Deformation of a General Class of Polynomials and its Properties

2018 ◽  
Vol 85 (1-2) ◽  
pp. 226
Author(s):  
Rajesh V. Savalia ◽  
B. I. Dave
Keyword(s):  
Differential Equation ◽  
Generating Function ◽  
Gamma Function ◽  
General Class ◽  
Combinatorial Identities ◽  
Inversion Theorem ◽  
Generalized Gamma ◽  
General Class Of Polynomials ◽  
Generalized Polynomial ◽  
Generalized Gamma Function

The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γ&lt;sub&gt;p&lt;/sub&gt; and Pochhammer p-symbol (x)&lt;sub&gt;n,p&lt;/sub&gt; due to Rafael Dıaz and Eddy Pariguan [Divulgaciones Mathematicas Vol.15, No. 2(2007), pp. 179-192]. We establish the inverse series relation of this extended polynomial with the aid of general inversion theorem. We also obtain the generating function relations and the differential equation. Certain <em>p</em>-deformed combinatorial identities are illustrated in the last section.

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