### 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 language | English |
---|---|

Pages (from-to) | 797-825 |

Number of pages | 29 |

Journal | Tokyo Journal of Mathematics |

Volume | 39 |

Issue number | 3 |

Publication status | Published - 2017 Mar 1 |

### Keywords

- Logarithmic solutions
- Painlevé equation

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Logarithmic solutions of the fifth painlevé equation near the origin'. Together they form a unique fingerprint.

## Cite this

Shimomura, S. (2017). Logarithmic solutions of the fifth painlevé equation near the origin.

*Tokyo Journal of Mathematics*,*39*(3), 797-825.