Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-24T00:00:19.846Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Growth of Solutions of Algebraic Differential Equations Whose Coefficients are Arbitrary Entire Functions1

Published online by Cambridge University Press:  22 January 2016

Steven Bank
Steven Bank*
Affiliation:
University of Illinois
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.

In this paper we treat the problem of determining the rate of growth of entire functions which are solutions of first order algebraic differential equations whose coefficients are arbitrary entire functions (i.e. equations of the form Ω(z, y, dy/dz) = 0, where Ω(z, y, dy/dz) = is a polynomial in y and dy/dz, whose coefficients fkJ(z) are entire functions).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 39 , August 1970 , pp. 107 - 117
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

Footnotes

1)

This research was supported in part by the National Science Foundation (GP 7374).

References

[1] Bank, S., On solutions of algebraic differential equations whose coefficients are entire functions of finite order, Ann. Mat. Pura Appl., 83 (1969), 175–184.Google Scholar
[2] Blumenthal, O., Principes de la théorie des fonctions entières d’ordre infini, Gauthier-Villars, Paris, 1910.Google Scholar
[3] Hille, E., Analytic Function Theory—Volume II, Ginn and Company, Boston, 1962.Google Scholar
[4] Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthiers-Villars, Paris, 1929.Google Scholar
[5] Saks, S. and Zygmund, A., Analytic Functions, Warsaw, 1952.Google Scholar
[6] Valiron, G., Fonctions Analytiques, Presses Universitaires de France, Paris, 1954.Google Scholar
[7] Valiron, G., Sur les fonctions entières vérifiant une classe d’équations différentielles, Bull. Soc. Math. France, 51 (1923), 33–45.Google Scholar
[8] Valiron, G., Lectures on the general theory of integral functions, Edouard Privat, Toulouse, 1923.Google Scholar
[9] Valiron, G., Les théorèmes généraux de M. Borel dans la théorie des fonctions entières, Ann. Ecole Norm., t. 37 (1920), 219–253.Google Scholar
[10] Wiman, A., Ueber den Zusammenhang zwischen dem Maximalbetrage einer analytischen Funktion und dem grössten Gliede der zugehörigen Taylorschen Reihe, Acta Math., 37 (1914), 305–326.Google Scholar
[11] Wiman, A., Ueber den Zusammenhang zwischen dem Maximalbetrage einer analytischen Funktion und dem grössten Betrage bei gegebenem Argumente der Funktion, Acta Math., 41 (1916), 1–28.Google Scholar