Coalescence of Two Regular Singularities into One Regular Singularity for the Linear Ordinary Differential Equation

Springer Science and Business Media LLC - Tập 7 - Trang 127-149 - 2001
A. Ya. Kazakov1
1Department of Higher Mathematics, State University of AeroSpace Instrumentation, S.-Petersburg, Russia

Tóm tắt

The process of coalescence of two regular singular points of linear ODE into a single regular singularity is studied. This problem is examined in terms of connection matrices and solutions of the corresponding equations.

Tài liệu tham khảo

D. I. Abramov and S. Yu. Slavyanov, The two Coulomb centers problem at small inter-center separations. J. Phys. B: Atom. Molec. Phys. 11 (1978), 2229–2241. W. Lay and S. Yu. Slavyanov, Heun's equation with nearby singularities. Proc. Roy. Soc. London A 455 (1999), 4347–4361. N. A. Veshev, Degeneration of solutions of Heun equation at coalescence of singularities. Teoret. Matem. Fiz. 110 (1997), 228–232. W. W. Golubev, Lectures on Analytic Theory of Differential Equations. (Russian) Moscow-Leningrad Gostekhizdat, 1941. M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations. (Russian) Moscow, Nauka, 1983. W. Vasov, Asymptotic expansions for ordinary differential eqiations. John Wiley, New York, 1965. E. Hille, Ordinary Differential Equations in the Complex Domain. New York, Dover Publications, Inc. Mineola, 1997. H. Bateman and A. Erdelyi, Higher Transcendental Functions, V l.1, New York, McGraw-Hill Book Comp., Inc., 1953. E. Titchmarsh, Function Theory. (Russian) Moscow, GITTL, 1951. R. Shäfke, Confluence of several regular points into irregular one. J. Dynam. Control Systems 4 (1998), No. 3, 401–424. A. A. Glutsuk, Stokes operators via limit monodromy of generic perturbation. J. Dynam. Control Systems 5 (1999), No. 1, 101–135.