Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T09:18:00.255Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic Solution Of Differential Equations In a Domain Containing a Regular Singular Point

Published online by Cambridge University Press:  20 November 2018

N. D. Kazarinoff  and
R. McKelvey
N. D. Kazarinoff
Affiliation:
Purdue University
R. McKelvey
Affiliation:
Institute for Fluid Dynamics and Applied Mathematics University of Maryland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Introduction. In this paper we study the asymptotic behavior in λ of the solutions about the origin in the z-plane of the differential equation

.

Both the variable z and the parameter λ are complex. The coefficient P(z, λ) is assumed to be analytic and single-valued in λ at infinity and in z throughout a bounded, closed, simply connected domain D containing z = 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 97 - 104
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Birkhoff, G. D., On the asymptotic character of the solutions of certain differential equations containing a parameter, Trans. Amer. Math. Soc, 9 (1908), 214–231.Google Scholar
2. Buchholz, H., Die konfluente hypergeometrische Funktion (Berlin, 1953).Google Scholar
3. Cashwell, E. D., The asymptotic solutions of an ordinary differential equation in which the coefficient of the parameter is singular, Pacific J. Math., 1 (1951), 337–352.Google Scholar
4. Evans, R. L., Solution of linear ordinary differential equations containing a parameter, Proc. Amer. Math. Soc. 4 (1953), 92–94.Google Scholar
5. Langer, R. E., The asymptotic solutions of ordinary linear differential equations, etc., Trans. Amer. Math. Soc, 67 (1949), 461–490.Google Scholar
6. Langer, R. E., On the asymptotic solutions of ordinary differential equations, etc., Trans. Amer. Math., Soc, 87 (1935), 397, et seq.Google Scholar