Second order differential equations with transcendental coefficients

Author:
John Rossi

Journal:
Proc. Amer. Math. Soc. **97** (1986), 61-66

MSC:
Primary 30D35; Secondary 34A20

DOI:
https://doi.org/10.1090/S0002-9939-1986-0831388-8

MathSciNet review:
831388

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Abstract: Let and be two linearly independent solutions to , where is a transcendental entire function of order . We show that the exponent of convergence of the zeros of is either infinite or satisfies . For , this answers a question of Bank.

**[1]**A Baernstein II,*Proof of Edrei's spread conjecture*, Proc. London Math. Soc. (3)**26**(1973), 418-434. MR**0374429 (51:10629)****[2]**S. Bank and I. Laine,*On the oscillation theory of**where**is entire*, Trans. Amer. Math. Soc.**273**(1982), 351-363. MR**664047 (83k:34009)****[3]**-,*On the zeros of meromorphic solutions of second order linear differential equations*, Comment. Math. Helv.**58**(1983), 656-677. MR**728459 (86a:34008)****[4]**A. Eremenko,*Growth of entire and meromorphic functions on asymptotic curves*, Sibirsk Mat. Zh.**21**(1980), 39-51; English transl. in Siberian Math. J. (1981), 673-683. MR**592215 (82i:30039)****[5]**L. C. Shen,*On a problem of Bank and Laine concerning the product of two linear independent solutions to*(to appear).**[6]**M. Tsuji,*Potential theory in modern function theory*, Maruzen, Tokyo, 1959. MR**0114894 (22:5712)**

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0831388-8

Article copyright:
© Copyright 1986
American Mathematical Society