ASYMPTOTIC EXPANSIONS AND STOKES MULTIPLIERS OF THE CONFLUENT HYPERGEOMETRIC FUNCTION PHI(2),IOTA

Authors
SHIMOMURA S
Citation
S. Shimomura, ASYMPTOTIC EXPANSIONS AND STOKES MULTIPLIERS OF THE CONFLUENT HYPERGEOMETRIC FUNCTION PHI(2),IOTA, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 123, 1993, pp. 1165-1177
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics → ACNP
ISSN journal
03082105
Volume
123
Year of publication
1993
Part
6
Pages
1165 - 1177
Database
ISI
SICI code
0308-2105(1993)123:<1165:AEASMO>2.0.ZU;2-B
Abstract
The confluent hypergeometric function Phi(2)(beta, beta', gamma , 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 = inf inity, y = infinity of irregular type. Near x = infinity (\y\ is bound ed) and near y = infinity (\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 Phi(2) (beta, beta', gamma, x, y) itself is also clarified near these singula r loci.