### Abstract

The confluent hypergeometric function Φ_{3} satisfies a system of partial differential equations on P^{1}(C) × P^{1} (C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

Original language | English |
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Pages (from-to) | 689-702 |

Number of pages | 14 |

Journal | International Journal of Mathematics |

Volume | 8 |

Issue number | 5 |

Publication status | Published - 1997 Aug |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A system associated with the confluent hypergeometric function Φ _{3} and a certain linear ordinary differential equation with two irregular singular points.** / Shimomura, Shun.

Research output: Contribution to journal › Article

_{3}and a certain linear ordinary differential equation with two irregular singular points',

*International Journal of Mathematics*, vol. 8, no. 5, pp. 689-702.

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TY - JOUR

T1 - A system associated with the confluent hypergeometric function Φ3 and a certain linear ordinary differential equation with two irregular singular points

AU - Shimomura, Shun

PY - 1997/8

Y1 - 1997/8

N2 - The confluent hypergeometric function Φ3 satisfies a system of partial differential equations on P1(C) × P1 (C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

AB - The confluent hypergeometric function Φ3 satisfies a system of partial differential equations on P1(C) × P1 (C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

UR - http://www.scopus.com/inward/record.url?scp=0031286953&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031286953&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031286953

VL - 8

SP - 689

EP - 702

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 5

ER -