Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation

Abstract

We apply the uniform asymptotics method proposed by Bassom et al. to a special Painlevé V equation, and we provide a simpler and more rigorous proof of the connection formulas for a special solution of the equation, which have been established earlier by McCoy and Tang via the isomonodromy and WKB methods.

Keywords:

• connection formula
• uniform asymptotics
• the fifth Painlevé transcendent
• parabolic cylinder function
• Bessel function

AMS Subject Classifications:

• 33E17
• 33C10
• 34E05

Additional information

Funding

Yu-Qiu Zhao was supported in part by the National Natural Science Foundation of China under [grant number 10871212].