### Abstract

The confluent hypergeometric function [formula omitted] satisfies a system of partial differential equations which possesses the singular loci [formula omitted] of regular type and [formula omitted]of irregular type. Near[formula omitted] is bounded) and near [formula omitted]is bounded), asymptotic expansions and Stokes multipliers of linearly independent solutions of the system are obtained. By a connection formula, the asymptotic behaviour of[formula omitted] itself is also clarified near these singular loci.

Original language | English |
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Pages (from-to) | 1165-1177 |

Number of pages | 13 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 123 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1993 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function ϕ I.** / Shimomura, Shun.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 123, no. 6, pp. 1165-1177. https://doi.org/10.1017/S0308210500029802

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TY - JOUR

T1 - Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function ϕ I

AU - Shimomura, Shun

PY - 1993

Y1 - 1993

N2 - The confluent hypergeometric function [formula omitted] satisfies a system of partial differential equations which possesses the singular loci [formula omitted] of regular type and [formula omitted]of irregular type. Near[formula omitted] is bounded) and near [formula omitted]is bounded), asymptotic expansions and Stokes multipliers of linearly independent solutions of the system are obtained. By a connection formula, the asymptotic behaviour of[formula omitted] itself is also clarified near these singular loci.

AB - The confluent hypergeometric function [formula omitted] satisfies a system of partial differential equations which possesses the singular loci [formula omitted] of regular type and [formula omitted]of irregular type. Near[formula omitted] is bounded) and near [formula omitted]is bounded), asymptotic expansions and Stokes multipliers of linearly independent solutions of the system are obtained. By a connection formula, the asymptotic behaviour of[formula omitted] itself is also clarified near these singular loci.

UR - http://www.scopus.com/inward/record.url?scp=84976189236&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84976189236&partnerID=8YFLogxK

U2 - 10.1017/S0308210500029802

DO - 10.1017/S0308210500029802

M3 - Article

AN - SCOPUS:84976189236

VL - 123

SP - 1165

EP - 1177

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 6

ER -