scholarly journals On hypergeometric functions in several variables II. The Wronskian of the hypergeometric functions of type $(n+1, m+1)$

1993 ◽  
Vol 45 (4) ◽  
pp. 645-669 ◽  
Author(s):  
Michitake KITA
Keyword(s):  
Hypergeometric Functions ◽  
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

scholarly journals On vanishing of the twisted rational de Rham cohomology associated with hypergeometric functions

1994 ◽  
Vol 135 ◽  
pp. 55-85 ◽  
Author(s):  
Michitake Kita
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
De Rham Cohomology ◽  
Direct Generalization ◽  
Several Variables ◽  
De Rham ◽  
Complex Powers

Recent development in hypergeometric functions in several variables has made the importance of studying twisted rational de Rham cohomology clear to many specialists. Roughly speaking, a hypergeometric function in our sense is the integral of a product of complex powers of polynomials Pj(u1, . . . . ,un) : ∫ U du1 ∧ · · · ∧ dun, U = Π , integration being taken over some cycle. So we are led naturally to consider the twisted rational de Rham cohomology, which is a direct generalization of the usual de Rham cohomology to multivalued case.

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