On a problem of Erdős concerning the zeros of the derivatives of an entire function

Authors:
K. F. Barth and W. J. Schneider

Journal:
Proc. Amer. Math. Soc. **32** (1972), 229-232

MSC:
Primary 30A66

DOI:
https://doi.org/10.1090/S0002-9939-1972-0293089-7

MathSciNet review:
0293089

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be any sequence of sets in the complex plane, each of which has no finite limit point. The authors prove, answering affirmatively a question posed by P. Erdös, that there exists a sequence of positive integers and a transcendental entire function such that if .

**[1]**P. Erdös and A. Rényi,*On the number of zeros of successive derivatives of analytic functions*, Acta Math. Acad. Sci. Hungar.**7**(1956), 125–144 (English, with Russian summary). MR**0080155**, https://doi.org/10.1007/BF02028197**[2]**P. Erdös and A. Rényi,*On the number of zeros of successive derivatives of entire functions of finite order*, Acta Math. Acad Sci. Hungar.**8**(1957), 223–225. MR**0088555**, https://doi.org/10.1007/BF02025245**[3]**W. K. Hayman,*Research problems in function theory*, The Athlone Press University of London, London, 1967. MR**0217268****[4]**J. L. Walsh,*Interpolation and approximation by rational functions in the complex domain*, Third edition. American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR**0218587**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0293089-7

Keywords:
Derivatives of an entire function,
interpolation in the complex plane

Article copyright:
© Copyright 1972
American Mathematical Society