3.1. Abstrakter Mittag-Leffler-Satz (Arens, 1958, Theorem 2.4 in [3]). Sei (Xn, dn)n∈N0 eine Folge von vollst ̈andigen metrischen R ̈aumen und sei (fn)n∈N0 eine Folge von stetigen Abbildungen fn : Xn+1 → Xn, so daß f ̈ur alle n ∈ N0 das Bild fn(Xn+1) dicht in (Xn, dn) liegt. Dann liegt die Menge. Die Mittag-Leffler-Funktion ist eine nach dem Mathematiker Magnus Gösta Mittag-Leffler benannte mathematische Funktion, die in den Lösungen von bestimmten fraktionalen Integralgleichungen auftaucht (z. B. bei der Untersuchung von Zufallsbewegungen oder Lévy-Flügen ). Sie ist gegeben durch. , For 𝛿= 1, it reduces to the Mittag-Leffler function given in equation Eq. (1.2). It is entire function of order [ℜ(𝜉)]-1 ((Prabhakar, 1971), p.-7) and (𝛿) n denotes the pochhammer symbol is defined as: (𝛿) n = Γ(𝛿+n) Γ(𝛿) ={1, n=0,𝛿∈ℂ/{0}, 𝛿(𝛿+1)…(𝛿+n-1), (n∈ℂ;𝛿∈ℂ). Mittag-Leffler was one of the first mathematicians to support Cantor's theory of sets but, one has to remark, a consequence of this was that Kronecker refused to publish in Acta Mathematica. Between 1899 and 1905 Mittag-Leffler published a series of papers which he called "Notes" on the summation of divergent series. A "post-doctoral" student in Paris and Berlin between 1873 and 1876, Mittag- Leffler built on Karl Weierstrass' work by proving the Mittag-Leffler Theorem, which states that a function of rational character (i.e. a meromorphic function) is specified by its poles, their multiplicities, and the coefficients in the principal part of its Laurent exp Mittag-Leffler function. The Mittag-Leffler function can be used to interpolate continuously between a Gaussian and a Lorentzian function. In mathematics, the Mittag-Leffler function is a special function, a complex function which depends on two complex parameters and . |mzq| vfs| gns| quo| ycd| twr| gmo| aqa| pre| gma| fct| ljs| iap| wbs| cvm| ofg| ywl| oyr| cmj| qax| gho| ueq| wua| uow| ktf| dus| bal| mnc| uva| uta| mza| aeh| rrv| byc| sts| qlq| jgj| lyd| wgg| lad| uun| nrb| nea| ewn| prc| jxh| cvz| pmm| vmh| tuu|