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

DOI10.1080/00036811.2015.1004322zbMath1334.33041arXiv1501.00337OpenAlexW2070713335WikidataQ58160991 ScholiaQ58160991MaRDI QIDQ2795472

Zhao-Yun Zeng, Yu-Qiu Zhao

Publication date: 21 March 2016

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00337

zbMATH Keywords

Bessel functionuniform asymptoticsparabolic cylinder functionconnection formulathe fifth Painlevé transcendent

Mathematics Subject Classification ID

Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Asymptotic expansions of solutions to ordinary differential equations (34E05) Painlevé-type functions (33E17)

Related Items (5)

On the connection problem for the second Painlevé equation with large initial data ⋮ Connection Problem of the First Painlevé Transcendent Between Poles and Negative Infinity ⋮ A note on the connection problem of some special Painlevé V functions ⋮ Irregular conformal blocks and connection formulae for Painlevé V functions ⋮ On the connection problem for nonlinear differential equation

Uses Software

• DLMF

Cites Work

• Monodromy problem and the boundary condition for some Painlevé equations
• The isomonodromic deformation method in the theory of Painlevé equations
• Connection formulae for Painlevé V functions
• Connection formulae for Painlevé V functions. II: the \(\delta\) function Bose gas problem
• Monodromy- and spectrum-preserving deformations. I
• Application of uniform asymptotics to the second Painlevé transcendent
• Level spacing distributions and the Bessel kernel
• Surfaces with harmonic inverse mean curvature and Painlevé equations
• Application of uniform asymptotics to the fifth Painlevé transcendent
• Connection formulae for Painlevé functions
• Application of uniform asymptotics method to analyzing the asymptotic behaviour of the general fourth Painlevé transcendent
• Asymptotic solutions of second-order linear differential equations having almost coalescent turning points, with an application to the incomplete gamma function
• Application of uniform asymptotica method to the asymptotics of the solutions of the fifth paonlevé equation when δ=0
• ON THE CONNECTION FORMULAS OF THE FOURTH PAINLEVÉ TRANSCENDENT
• Second-order linear differential equations with two turning points
• Painlevé functions of the third kind
• Connection formulae for asymptotics of the fifth Painlevé transcendent on the real axis

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