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March 2017 Logarithmic Solutions of the Fifth Painlevé Equation near the Origin
Shun SHIMOMURA
Tokyo J. Math. 39(3): 797-825 (March 2017). DOI: 10.3836/tjm/1475723087

Abstract

For the fifth Painlevé equation near the origin we present two kinds of logarithmic solutions, which are represented, respectively, by convergent series with multipliers admitting asymptotic expansions in descending logarithmic powers and by those with multipliers polynomial in logarithmic powers. It is conjectured that the asymptotic multipliers are also polynomials in logarithmic powers. These solutions are constructed by iteration on certain rings of exponential type series.

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Shun SHIMOMURA. "Logarithmic Solutions of the Fifth Painlevé Equation near the Origin." Tokyo J. Math. 39 (3) 797 - 825, March 2017. https://doi.org/10.3836/tjm/1475723087

Information

Published: March 2017
First available in Project Euclid: 6 October 2016

zbMATH: 1370.34145
MathSciNet: MR3634294
Digital Object Identifier: 10.3836/tjm/1475723087

Subjects:
Primary: 34M55
Secondary: 34M30, 34M35

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.39 • No. 3 • March 2017
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