A note on the connection problem of some special Painlev\'e V functions
Wen-Gao Long, Zhao-Yun Zeng, Jian-Rong Zhou
TL;DR
This paper uses the method of uniform asymptotics to provide a simpler, more rigorous proof of connection formulas for special solutions of the fifth Painlevé equation, building on previous work by Andreev and Kitaev.
Contribution
It introduces a new application of uniform asymptotics to rigorously prove connection formulas for special Painlevé V solutions, simplifying earlier proofs.
Findings
Established more rigorous connection formulas for Painlevé V solutions.
Demonstrated the effectiveness of uniform asymptotics in this context.
Simplified the proof process compared to previous methods.
Abstract
As a new application of the method of "uniform asymptotics" proposed by Bassom, Clarkson, Law and McLeod, we provide a simpler and more rigorous proof of the connection formulas of some special solutions of the fifth Painlev\'e equation, which have been established earlier by Andreev and Kitaev.
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