Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T11:39:19.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Entire solutions of linear differential equations and bounds for growth and index numbers

Published online by Cambridge University Press:  14 November 2011

S. M. Shah
S. M. Shah
Affiliation:
University of Kentucky, Lexington, KY 40506, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper entire solutions of differential equations with polynomial coefficients are considered and bounds on the maximum modulus and the index are obtained, when the equation is of second order and the coefficients are of second degree.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 49 - 60
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Abramowitz, M. and Stegun, I. A. (Eds) Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C.; 1964).Google Scholar
2Beauchamp, J. P.. Inégalités différentielles et distribution des valuers en analyse complexe (Doctoral dissertation, Univ. de Montreal, 1978).Google Scholar
3Fricke, G. H. and Shah, S. M.. On bounded value distribution and bounded index. J. Nonlinear Analysis 2 (1978), 423–436.CrossRefGoogle Scholar
4Fricke, G. H., Ray, R. and Shah, S. M.. Bounded index, entire solutions of ordinary differential equations and summability methods. Intemat. J. Math. Sci. 4 (1981), 417–434.CrossRefGoogle Scholar
5Hayman, W. K.. Differential inequalities and local valency. Pacific J. Math. 44 (1973), 117–137.CrossRefGoogle Scholar
6Hennekemper, W., Some results of functions of bounded index. Lecture Notes in Mathematics 747, 158–160 (Berlin: Springer, 1978).Google Scholar
7Lee, Boo Sang and Shah, S. M.. The type of an entire function satisfying a linear differential equation. Arch. Math 20 (1969), 616–622.CrossRefGoogle Scholar
8Lee, Boo Sang and Shah, S. M.. An inequality involving the Bessel Function and its derivatives. J. Math. Anal. Appl. 30 (1970), 144–155.CrossRefGoogle Scholar
9Lepson, B.. Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index. Proc. Sympos. Pure Math. Vol. XI, 298–307 (Providence, R.I.: Amer. Math. Soc, 1968).Google Scholar
10Rees, C. S., Shah, S. M. and Stanojevic, C. V.. Theory and Applications of Fourier Analysis (Marcel Dekker, New York: 1981).Google Scholar
11Marie, V. and Shah, S. M.. Entire functions defined by gap power series and satisfying a differential equation. Tôhoku Math. J. 21 (1969), 621–631.Google Scholar
12Shah, S. M.. Entire functions of bounded index. Proc. Amer. Math. Soc. 19 (1968), 1017–1022.CrossRefGoogle Scholar
13Shah, S. M.. Entire functions satisfying a linear differential equation. J. Math. Mech. 18 (1968/1969), 131–136.Google Scholar
14Shah, S. M.. Entire functions of bounded index. Lecture Notes in Mathematics 599, 117–145 (Berlin: Springer, 1977).Google Scholar
15Valiron, Georges. Lectures on the General Theory of Integral Functions (New York: Chelsea, 1949).Google Scholar
16Whittaker, J. M.. An inequality involving derivatives. Bull. London Math. Soc. 2 (1970), 297–300.CrossRefGoogle Scholar
17Wittich, Hans. Neuere Untersuchungen Über Eindeutige Analytische Funktionen (Berlin: Springer, 1955).CrossRefGoogle Scholar