Asymptotic Analysis for Integrable Connections with Irregular Singular Points

1984 ◽  
Author(s):  
Hideyuki Majima
Keyword(s):  
Asymptotic Analysis ◽  
Singular Points ◽  
Irregular Singular Points

A System Associated with the Confluent Hypergeometric Function Φ3 and a Certain Linear Ordinary Differential Equation with Two Irregular Singular Points

1997 ◽  
Vol 08 (05) ◽  
pp. 689-702 ◽  
Author(s):  
Shun Shimomura
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Hypergeometric Function ◽  
Confluent Hypergeometric Function ◽  
Linear Ordinary Differential Equation ◽  
Singular Points ◽  
Third Order ◽  
Regular Type ◽  
Singular Loci ◽  
Irregular Singular Points

The confluent hypergeometric function Φ3 satisfies a system of partial differential equations on P1(C) × P1(C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

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