ON PARTICULAR SOLUTIONS OF THE GARNIER SYSTEMS AND THE HYPERGEOMETRIC FUNCTIONS OF SEVERAL VARIABLES

1986 ◽  
Vol 37 (1) ◽  
pp. 61-80 ◽  
Author(s):  
KAZUO OKAMOTO ◽  
HIRONOBU KIMURA
Keyword(s):  
Hypergeometric Functions ◽  
Particular Solutions ◽  
Several Variables

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.

Singularities of hypergeometric functions in several variables

2005 ◽  
Vol 141 (03) ◽  
pp. 787-810 ◽  
Author(s):  
Mikael Passare ◽  
Timur Sadykov ◽  
August Tsikh
Keyword(s):  
Hypergeometric Functions ◽  
Several Variables

Particular solutions of equations with multiple characteristics expressed through hypergeometric functions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Bahrom Y. Irgashev
Keyword(s):  
Hypergeometric Functions ◽  
Model Equation ◽  
Fundamental Solutions ◽  
Similarity Solutions ◽  
Arbitrary Integer ◽  
Integer Order ◽  
Particular Solutions ◽  
Multiple Characteristics ◽  
Solutions Of Equations

Abstract In the paper, similarity solutions are constructed for a model equation with multiple characteristics of an arbitrary integer order. It is shown that the structure of similarity solutions depends on the mutual simplicity of the orders of derivatives with respect to the variable x and y, respectively. Frequent cases are considered in which they are shown as fundamental solutions of well-known equations, expressed in a linear way through the constructed similarity solutions.

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