Logarithmic solutions of the fifth painlevé equation near the origin

Shun Shimomura

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)797-825
Number of pages29
JournalTokyo Journal of Mathematics
Volume39
Issue number3
Publication statusPublished - 2017 Mar 1

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Logarithmic
Multiplier
Polynomial
Exponential Type
Series
Asymptotic Expansion
Iteration
Ring

Keywords

  • Logarithmic solutions
  • Painlevé equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Logarithmic solutions of the fifth painlevé equation near the origin. / Shimomura, Shun.

In: Tokyo Journal of Mathematics, Vol. 39, No. 3, 01.03.2017, p. 797-825.

Research output: Contribution to journalArticle

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