On the zeros of successive derivatives of even Laguerre-Pólya functions
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- by Li-Chien Shen PDF
- Trans. Amer. Math. Soc. 298 (1986), 643-652 Request permission
Abstract:
Using "method of steepest descent", we prove that the final set (in the sense of Polya) of a class of even Laguerre-Polya functions is the entire real axis.References
- W. K. Hayman, A generalisation of Stirling’s formula, J. Reine Angew. Math. 196 (1956), 67–95. MR 80749, DOI 10.1515/crll.1956.196.67
- Simon Hellerstein and Jack Williamson, Derivatives of entire functions and a question of Pólya, Trans. Amer. Math. Soc. 227 (1977), 227–249. MR 435393, DOI 10.1090/S0002-9947-1977-0435393-4
- Simon Hellerstein and Jack Williamson, Derivatives of entire functions and a question of Pólya. II, Trans. Amer. Math. Soc. 234 (1977), no. 2, 497–503. MR 481004, DOI 10.1090/S0002-9947-1977-0481004-1
- B. Ja. Levin, Distribution of zeros of entire functions, Revised edition, Translations of Mathematical Monographs, vol. 5, American Mathematical Society, Providence, R.I., 1980. Translated from the Russian by R. P. Boas, J. M. Danskin, F. M. Goodspeed, J. Korevaar, A. L. Shields and H. P. Thielman. MR 589888
- G. Polya, On the zeros of the derivatives of a function and its analytic character, Bull. Amer. Math. Soc. 49 (1943), 178–191. MR 7781, DOI 10.1090/S0002-9904-1943-07853-6
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 298 (1986), 643-652
- MSC: Primary 30D15; Secondary 30C15
- DOI: https://doi.org/10.1090/S0002-9947-1986-0860385-6
- MathSciNet review: 860385