Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T03:37:58.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function Φ2, I

Published online by Cambridge University Press:  14 November 2011

Shun Shimomura
Shun Shimomura
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama 223, Japan
Get access Rights & Permissions [Opens in a new window]

Synopsis

The confluent hypergeometric function Φ2(β,β′, γ, x, y) satisfies a system of partial differential equations which possesses the singular loci x = 0, y = 0, x − y = 0 of regular type and x = ∞, y = ∞ of irregular type. Near x = ∞ (|y| is bounded) and near y = ∞ (|x| is bounded), asymptotic expansions and Stokes multipliers of linearly independent solutions of the system are obtained. By a connection formula, the asymptotic behaviour of Φ2(β,β′, γ, x, y) itself is also clarified near these singular loci.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1165 - 1177
Copyright
Copyright © Royal Society of Edinburgh 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Erdélyi, A.. Integration of a certain system of linear partial differential equations of hypergeometric type. Proc. Roy. Soc. Edinburgh 59 (1939), 224–241.CrossRefGoogle Scholar
2Erdelyi, A.. Some confluent hypergeometric functions of two variables. Proc. Roy. Soc. Edinburgh 60(1940), 344–361.CrossRefGoogle Scholar
3Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.. Higher Transcendental Functions, Vols 1 and 2 (New York: McGraw-Hill, 1953).Google Scholar
4Majima, H.. Stokes structure of the confluent hypergeometric differential equations in two variables and resurgent equations (preprint).Google Scholar
5Wasow, W.. Asymptotic Expansions for Ordinary Differential Equations (New York: Interscience, 1965).Google Scholar