Logarithmic solutions of the fifth painlevé equation near the origin

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2017 Mar 1


  • Logarithmic solutions
  • Painlevé equation

ASJC Scopus subject areas

  • General Mathematics


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