scholarly journals Properties of k-beta function with several variables

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Abdur Rehman ◽  
Shahid Mubeen ◽  
Rabia Safdar ◽  
Naeem Sadiq
Keyword(s):  
Beta Function ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Function Of Two Variables

AbstractIn this paper, we discuss some properties of beta function of several variables which are the extension of beta function of two variables. We define k-beta function of several variables and derive some properties of this function which are the extension of k-beta function of two variables, recently defined by Diaz and Pariguan [4]. Also, we extend the formula Γ

scholarly journals A Study of I-Function of Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Prathima Jayarama ◽  
Vasudevan Nambisan Theke Madam ◽  
Shantha Kumari Kurumujji
Keyword(s):  
Natural Generalization ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Generalized Function ◽  
Several Variables ◽  
Special Cases ◽  
Function Of Several Variables ◽  
Function Of Two Variables

The aim of this paper is to introduce a natural generalization of the well-known, interesting, and useful Fox H-function into generalized function of several variables, namely, the I-function of ‘‘r’’ variables. For r=1, we get the I-function introduced and studied by Arjun Rathie (1997) and, for r=2, we get I-function of two variables introduced very recently by ShanthaKumari et al. (2012). Convergent conditions, elementary properties, and special cases have also been given. The results presented in this paper generalize the results of H-function of ‘‘r’’ variables available in the literature.

On The Factorization of Partial Differential Equations

1987 ◽  
Vol 39 (4) ◽  
pp. 825-834 ◽  
Author(s):  
W. Dale Brownawell
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nevanlinna Theory ◽  
Algebraic Differential Equation ◽  
List Type ◽  
Variable Result ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Degenerate Cases

In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F. Gross in [2].) The thrust of Steinmetz’ central results on factorization is that if g(z) is entire and f(z) is meromorphic in C such that the composite fog satisfies an algebraic differential equation, then so do f(z) and, degenerate cases aside, g(z). In addition, the more one knows about the equation for fog (e.g. degree, weight, autonomy), the more one can conclude about the equations for f and g.In this note we generalize Steinmetz’ work to show the following:a) Steinmetz’ two basic results, Satz 1 and Korollar 1 of [4] can be seen as one-variable specializations of a single two variable result, andb) the function g(z) can itself be allowed to be a function of several variables.

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