54 research outputs found
Power expansions for solution of the fourth-order analog to the first Painlev\'{e} equation
One of the fourth-order analog to the first Painlev\'{e} equation is studied.
All power expansions for solutions of this equation near points and
are found by means of the power geometry method. The exponential
additions to the expansion of solution near are computed. The
obtained results confirm the hypothesis that the fourth-order analog of the
first Painlev\'{e} equation determines new transcendental functions.Comment: 28 pages, 5 figure
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