Integral representations and asymptotic behaviours of Mittag-Leffler type functions of two variables

Christian Lavault (1)

1 LIPN - Laboratoire d'Informatique de Paris-Nord

The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values of the parameters are obtained. The asymptotic expansions formulas and asymptotic properties of such functions are also established for large values of the variables. This provides statements of theorems for these formulas and their corresponding properties.

Mots clés: Generalized two-parametric Mittag-Leffler type functions of two variables; Integral representations; Special functions; Hankel's integral contour; Asymptotic expansion formulas

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]; Analyse classique [math.CA]

Christian Lavault. Integral representations and asymptotic behaviours of Mittag-Leffler type functions of two variables. 2017. ⟨hal-01522850⟩