Power expansions of solutions to an
analogy to the first Painleve' equation
We consider an ordinary differential equation of the fourth order, which is
the first analogy to the first Painlev'e equation.
By methods of Power Geometry, we find all power expansions of its solution
near points z=0 and z=∞. For expansions of solutions
near z=∞, we calculate exponential additions of the first, second and
third levels. Our results confirm the conjecture that the equation
determines new transcendetal functions. We also describe an algorithm of
computation of a basis of a minimal lattice, containing a given finite set.
Mathematical problems and theory of numerical methods