References
M. M. Dzhrbashyan, Integral Transforms and Representation of Functions in a Complex Domain [in Russian], Moscow (1966).
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).
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).
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).
I. V. Ostrovski and I. N. Pereselkova, “Nonasymptotic results on distribution of zeros of the function E ρ (z, μ),” Anal. Math., 23, 283–296 (1997).
G. Polya, “Bemerkung über die Mittag-Lefferschen Funktionen E α (z),” Tôhoku Math. J., 19, 241–248 (1921).
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).
A. M. Sedletskii, “Asymptotic formulas for zeros of a Mittag-Leffer-type function,” Anal. Math., 20, 117–132 (1994).
E. D. Solomentsev, “Mittag-Leffer function,” in: Mathematical Encyclopedia, Vol. 3 [in Russian], Moscow (1982), p. 707.
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).
A. Wiman, “Über die Nullstellen der Funktionen E α (x),” Acta Math., 29, 217–234 (1905).
Additional information
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 35, Voronezh Conference-2, 2005.
Rights and permissions
About this article
Cite this article
Popov, A.Y. On zeros of a certain family of Mittag-Leffler functions. J Math Sci 144, 4228–4231 (2007). https://doi.org/10.1007/s10958-007-0263-6
Issue Date:
DOI: https://doi.org/10.1007/s10958-007-0263-6