Second order differential equations with transcendental coefficients

Author:
John Rossi

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

MSC:
Primary 30D35; Secondary 34A20

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]**Albert Baernstein II,*Proof of Edrei’s spread conjecture*, Proc. London Math. Soc. (3)**26**(1973), 418–434. MR**0374429****[2]**Steven B. Bank and Ilpo Laine,*On the oscillation theory of 𝑓′′+𝐴𝑓=0 where 𝐴 is entire*, Trans. Amer. Math. Soc.**273**(1982), no. 1, 351–363. MR**664047**, 10.1090/S0002-9947-1982-0664047-6**[3]**Steven B. Bank and Ilpo Laine,*On the zeros of meromorphic solutions and second-order linear differential equations*, Comment. Math. Helv.**58**(1983), no. 4, 656–677. MR**728459**, 10.1007/BF02564659**[4]**A. È. Erëmenko,*The growth of entire and subharmonic functions on asymptotic curves*, Sibirsk. Mat. Zh.**21**(1980), no. 5, 39–51, 189 (Russian). MR**592215****[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 Co., Ltd., Tokyo, 1959. MR**0114894**

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

Article copyright:
© Copyright 1986
American Mathematical Society