Geodesic
On the real zeros of functions of Mittag-Leffler type
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 592-599

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In the present paper, we prove an assertion allowing us to extend results related to the presence or absence of real zeros of functions of Mittag-Leffler type $$ E_{1/\alpha}(z;\mu)=\sum_{k=0}^\infty\frac{z^k}{\Gamma(\alpha k+\mu)} $$ for certain values of $\alpha$ and $\mu$ to more extensive ranges of these parameters. We give a geometric description of the sets of pairs $(\alpha,\mu)$ for which the function $E_{1/\alpha}(z;\mu)$ has and does not have real zeros. 
@article{MZM_2005_77_4_a11,
     author = {A. V. Pskhu},
     title = {On the real zeros of functions of {Mittag-Leffler} type},
     journal = {Matemati\v{c}eskie zametki},
     pages = {592--599},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a11/}
}
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A. V. Pskhu. On the real zeros of functions of Mittag-Leffler type. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 592-599. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a11/