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References
M. Ålander, Sur le déplacement des zéros des fonctions entières par leur dérivation, Thèse, Uppsala, 1914.
M. Ålander, Sur les zéros extraordinaires des dérivées des fonctions entières réelles, Ark. Mat. Astronom. Fys. 11 (1916), No. 15.
A. Edrei, Meromorphic functions with three radially distributed values, Trans. Amer. Math. Soc. 78 (1955), 276–293.
G. Gundersen, On the real zeros of solutions of f″+A(z)f=0 where A(z) is entire, Annal. Acad. Sci. Fenn. (to appear).
S. Hellerstein and J. Rossi, Zeros of meromorphic solutions of second order linear differential equations, Math. Zeit. 192 (1986), 603–612.
S. Hellerstein and J. Williamson, Erivatives of entire functions and a question of Pólya, Trans.Amer. Math. Soc. 227 (1977), 227–247.
S. Hellerstein and J. Williamson, Derivatives of entire functions and a question of Pólya II, Trans. Amer. Math. Soc. 234 (1977), 497–503.
S. Hellerstein and J. Williamson, The zeros of the second derivative of the reciprocal of an entire function, Trans. Amer. Math. Soc. 263 (1981), 501–513.
S. Hellerstein, L.C. Shen, and J. Williamson, Reality of the zeros of an entire function and its derivatives, Trans Amer. Math. Soc. 275 (1983), 219–231.
S. Hellerstein, L.C. Shen, and J. Williamson, Real zeros of derivatives and solutions of second order differential equations, Trans. Amer. Math. Soc. 285 (1984), 759–776.
E. Hille, Oscillation theorems in the complex domain, Trans. Amer. Math. Soc. 23 (1922), 350–385.
E. Hille, Lectures on ordinary differential equations, Addison-Wesley, London, 1969.
W.P. Kohs, Derivatives of meromorphic functions and solutions to second order differential equations with rational coefficients, Dissertation, University of Hawaii, 1986.
B. Ja. Levin and I.V. Ostrovskii, The dependence of the growth of an entire function on the distribution of the zeros of its derivatives, Amer. Math. Soc. Transl. (2) 32 (1963), 322–357.
G. Pólya, Über Annäherung durch Polynome mit lauter reellen Wurzeln, Rend. Circ. Mat. Palermo 36 (1913), 279–295.
G. Pólya, Sur une question concernant les fonctions entières, C.R. Acad.Sci. Paris 158 (1914), 330–333.
G. Pólya, Bemerkung zur Theorie der ganzen Funktionen, Jber. Deutsch. Math.-Verein 24 (1915), 392–400.
G. Pólya, Über die Nullstellen sukzessiver derivierten, Math. Zeit. 12 (1922), 36–60.
G. Pólya, and G. Szego, Aufgaben und Lehrsatze aus der Analysis, Springer-Verlag, Berlin (1954).
J. Rossi, The reciprocal of an entire function of infinite order and the distribution of the zeros of its second derivative, Trans. Amer. Math. Soc. 270 (1982), 667–683.
L.C. Shen, Influence of the distribution of the zeros of an entire function and its second derivative on the growth of the function, Proc. London Math. Soc. (to appear).
H. Wittich, Neure untersuchungen über eindeutige analytische Functionen, 2nd ed., Springer-Verlag, Berlin (1968).
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Hellerstein, S. (1987). Real zeros of derivatives of meromorphic functions and solutions of differential equations — A survey with problems and conjectures. In: Berenstein, C.A. (eds) Complex Analysis I. Lecture Notes in Mathematics, vol 1275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078352
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DOI: https://doi.org/10.1007/BFb0078352
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