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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
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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.

Information

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

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References

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