Power solution expansions of the analogue tothe first Painleve equation
Abstract
The fourth-order analog to the first Painlev\'e equation is studied. All power expansions for solutions of this equation near points z=0 and z=∞ are found. 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 Painlev\'e equation determines new transcendental functions. By means of the methods of power geometry the basis of the plane lattice is also calculated.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.