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