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On the question of whether f″+ e−zf′ + B(z)f = 0 can admit a solution f ≢ 0 of finite order

Published online by Cambridge University Press:  14 November 2011

Gary G. Gundersen
Gary G. Gundersen
Affiliation:
Department of Mathematics, University of New Orleans, New Orleans, Louisiana 70148, U.S.A
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Synopsis

We show that if B(z) is either (i) a transcendental entire function with order (B)≠1, or (ii) a polynomial of odd degree, then every solution f≠0 to the equation f″ + e−zf′ + B(z)f = 0 has infinite order. We obtain a partial result in the case when B(z) is an even degree polynomial. Our method of proof and lemmas for case (i) of the above result have independent interest.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 1-2 , 1986 , pp. 9 - 17
Copyright
Copyright © Royal Society of Edinburgh 1986

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