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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.

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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