Geodesic
On the real zeros of functions of Mittag-Leffler type
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 592-599 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2005},
     volume = {77},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a11/}
}
TY  - JOUR
AU  - A. V. Pskhu
TI  - On the real zeros of functions of Mittag-Leffler type
JO  - Matematičeskie zametki
PY  - 2005
SP  - 592
EP  - 599
VL  - 77
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a11/
LA  - ru
ID  - MZM_2005_77_4_a11
ER  - 
%0 Journal Article
%A A. V. Pskhu
%T On the real zeros of functions of Mittag-Leffler type
%J Matematičeskie zametki
%D 2005
%P 592-599
%V 77
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a11/
%G ru
%F MZM_2005_77_4_a11
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/

[1] Popov A. Yu., Sedletskii A. M., “Raspredelenie nulei funktsii Mittag-Lefflera”, Dokl. RAN, 390:2 (2003), 165–168 | MR | Zbl

[2] Sedletskii A. M., “Neasimptoticheskie svoistva kornei funktsii tipa Mittag-Lefflera”, Matem. zametki, 75:3 (2004), 405–420 | MR

[3] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003 | Zbl

[4] Pskhu A. V., “Integralnoe preobrazovanie s funktsiei Raita v yadre”, Dokl. Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 6:1 (2002), 35–47

[5] Stankovich B., “O jednoj klasi singularnikh integralnikh jednachina”, Zbornik radova SAN. 43. Matematichki institut SAN, 4 (1955), 81–130

[6] Wright E. M., “The generalized Bessel function of order greater than one”, Quart. J. Math. (Oxford), 11 (1940), 36–48 | DOI | MR | Zbl

[7] Pskhu A. V., “Reshenie kraevoi zadachi dlya uravneniya s chastnymi proizvodnymi drobnogo poryadka”, Differents. uravneniya, 39:8 (2003), 1092–1099 | MR | Zbl

[8] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987 | MR

[9] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[10] Stanković B., “On the function of E. M. Wright”, Publs Inst. Math. Beograde, 10:24 (1970), 113–124 | MR | Zbl