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

Shun Shimomura

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)689-702
Number of pages14
JournalInternational Journal of Mathematics
Volume8
Issue number5
Publication statusPublished - 1997 Aug

Fingerprint

Confluent Hypergeometric Function
Linear Ordinary Differential Equations
Singular Point
Locus
Irregular
Systems of Partial Differential Equations
Stokes
Multiplier
Asymptotic Expansion
Linearly

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

@article{794c33f577304968a0893599ead59203,
title = "A system associated with the confluent hypergeometric function Φ3 and a certain linear ordinary differential equation with two irregular singular points",
abstract = "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.",
author = "Shun Shimomura",
year = "1997",
month = "8",
language = "English",
volume = "8",
pages = "689--702",
journal = "International Journal of Mathematics",
issn = "0129-167X",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "5",

}

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 -