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On zeros of a certain family of Mittag-Leffler functions. (English. Russian original) Zbl 1181.33019

J. Math. Sci., New York 144, No. 4, 4228-4231 (2007); translation from Sovrem. Mat. Prilozh. 35 (2005).
From the paper: The main result is the statement that all zeros of the Mittag-Leffler functions \(E_{1/N}(z,N+1)\), \(N\in\mathbb N\), \(N\geq 3\), are real, simple and belong to the ray \((-\infty,-(2N)!/N!)\).

MSC:

33E12 Mittag-Leffler functions and generalizations
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References:

[1] M. M. Dzhrbashyan, Integral Transforms and Representation of Functions in a Complex Domain [in Russian], Moscow (1966). · Zbl 0148.30002
[2] M. M. Dzhrbashyan and A. B. Nersesyan, ”On construction of certain special biorthogonal systems,” Izv. Akad. Nauk Arm. SSR, Ser. Mat., 12, 17–42 (1959).
[3] M. M. Dzhrbashyan, Boundary-value problem for a differential operator of fractional order of the Sturm-Liouville type,” Izv. Akad. Nauk ArmSSR, Ser. Mat., 5, 71–96 (1970). · Zbl 0212.43202
[4] A. M. Nakhushev, ”Sturm-Liouville problem for a differential equation of second order with fractional derivatives in the lower-order terms,” Dokl. Akad. Nauk SSSR, 234, 308–311 (1077).
[5] I. V. Ostrovski and I. N. Pereselkova, ”Nonasymptotic results on distribution of zeros of the function E {\(\rho\)} (z, {\(\mu\)}),” Anal. Math., 23, 283–296 (1997). · Zbl 0905.30004
[6] G. Polya, ”Bemerkung über die Mittag-Lefferschen Funktionen E {\(\alpha\)} (z),” Tôhoku Math. J., 19, 241–248 (1921).
[7] A. Yu. Popov, ”On eigenvalues of one boundary-value problem and zeros of the Mittag-Leffer function,” Differ. Equations, 38, No. 5, 611–621 (2002). · Zbl 1035.34096
[8] A. M. Sedletskii, ”Asymptotic formulas for zeros of a Mittag-Leffer-type function,” Anal. Math., 20, 117–132 (1994). · Zbl 0798.30023
[9] E. D. Solomentsev, ”Mittag-Leffer function,” in: Mathematical Encyclopedia, Vol. 3 [in Russian], Moscow (1982), p. 707.
[10] I. V. Tikhonov and Yu. S. Eidel’man, ”Inverse problems for differential equations in Banach spaces and distributions of zeros of Mittag-Leffer-type functions,” Differ. Equations, 38, No. 5, 637–644 (2002). · Zbl 1033.34017
[11] A. Wiman, ”Über die Nullstellen der Funktionen E {\(\alpha\)} (x),” Acta Math., 29, 217–234 (1905). · JFM 36.0472.01
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