On zeros of functions of Mittag-Leffler typeстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:As is well known, the asymptotics of zeros of functions of Mittag-Leffler type E rho (z ; mu) = Sigma (infinity)(n=0) z(n)/(Gamma(mu +n/p)), rho > 0, mu epsilon C describes the behavior of zeros outside a disk of sufficiently large radius. In the paper we solve the problem of finding the number of zeros inside such a disk; this allows us to indicate the numeration of all zeros E-rho(z ; mu) that agrees with tlne asymptotics. We study the problem of the distribution of zeros of two functions that call be expressed in terms of E-1(z ; mu), namely of the incomplete gamma-function and of the error function.