On zeros of a certain family of Mittag-Leffler functions

Mittag-Leffler Functions, Related Topics and Applications

“…One more immediate consequence of the results in [Sed94,Sed00,Sed04,Sed07] (see also [Pop02,Pop06,PopSed03]) is the fact that E˛;ˇwith˛> 0;ˇ2 R, is a function of completely regular growth in the sense of Levin-Pfluger.…”

“…We also mention here the treatise on complex functions by Sansone and Gerretsen [SanGer60], where a detailed account of these functions is given. 3.4-3.6 we have followed the monograph [Dzh66] and the survey paper [PopSed11]. We also mention another book by this author from 1993 [Djr93], in English, where a brief description of the theory of Mittag-Leffler functions is given.…”

“…In this section we mainly follow the article [Sed94] (see also [PopSed11]). First of all we recall some relations of the Mittag-Leffler function to elementary functions for special values of the parameters˛;ˇ.…”

“…In case (2) one can use a similar argument (see [PopSed11,) based on the following asymptotic formula…”

The Role of the Mittag-Leffler Function in Fractional Modeling

“…3-6), in particular different types of recurrence relations, integral and differential properties. The study of zeros' distribution is presented there, too (see also [42]). These results are helpful for the investigation of certain inverse scattering problems, as well as other problems from the operator theory.…”