Search

A numerical algorithm for calculating the generalized Mittag-Leffler Eα,≈(z) function for arbitrary complex argument z and real parameters α > 0 and β ϵ ℝ is presented. The algorithm uses the Taylor series, the exponentially improved asymptotic series, and integral representations to obtain optimal stability and accuracy of the algorithm. Special care is applied to the limits of validity of the different schemes to avoid instabilities in the algorithm. [ABSTRACT FROM AUTHOR]

We investigate the class of ±1 polynomials evaluated at q defined as: A(q) = {ϵ0 + ϵ1q + … + ϵmqm : ϵi Є {-1, 1}} and usually called spectrum, and show that, if q is the root of the polynomial xn - xn-1 - … - xk+1 + xk + xk-1 + … + x + 1 between 1 and 2, and n > 2k + 3, then A(q) is discrete, which means that it does not have any accumulation points. [ABSTRACT FROM AUTHOR]