### Abstract

The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel functions. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference analog of the Painlevé III equation.

Original language | English |
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Pages (from-to) | 4162-4174 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 36 |

Issue number | 8 |

DOIs | |

Publication status | Published - Jan 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*36*(8), 4162-4174. https://doi.org/10.1063/1.531353

**Casorati determinant solutions for the discrete Painlevé III equation.** / Kajiwara, Kenji; Ohta, Yasuhiro; Satsuma, Junkichi.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 36, no. 8, pp. 4162-4174. https://doi.org/10.1063/1.531353

}

TY - JOUR

T1 - Casorati determinant solutions for the discrete Painlevé III equation

AU - Kajiwara, Kenji

AU - Ohta, Yasuhiro

AU - Satsuma, Junkichi

PY - 1995/1/1

Y1 - 1995/1/1

N2 - The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel functions. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference analog of the Painlevé III equation.

AB - The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel functions. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference analog of the Painlevé III equation.

UR - http://www.scopus.com/inward/record.url?scp=36449008203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36449008203&partnerID=8YFLogxK

U2 - 10.1063/1.531353

DO - 10.1063/1.531353

M3 - Article

AN - SCOPUS:36449008203

VL - 36

SP - 4162

EP - 4174

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

ER -