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Regular version of the site

Book chapter

Chapter 5. Asymptotic expansions of solutions to the fifth Painlevé equation

P. 33-38.

By means of Power Geometry we obtained all asymptotic expansions of solutions to the equation P5 of the following five types: power, power-logarithmic, complicated, exotic, and half-exotic, for all values of complex parameters of the equations. They form 16 and 30 families in the neighborhoods of singularpoints z=\infty and z=0, respectively. There are 10 families in the neighborhood of a nonsingular point. Over 20 families are new.

In book

Chapter 5. Asymptotic expansions of solutions to the fifth Painlevé equation
Berlin: De Gruyter, 2012.