Power expansions for solution of the fourth-order analog to the first Painlevé equation

One of the fourth-order analog to the first Painlevé equation is studied. All power expansions for solutions of this equation near points z = 0 and z = ∞ are found by means of the power geometry method. The exponential additions to the expansion of solution near z = ∞ are computed. The obtained results confirm the hypothesis that the fourth-order analog of the first Painlevé equation determines new transcendental functions.