On the Graf's addition theorem for Hahn Exton q-Bessel function

Lazhar Dhaouadi (1) , Ahmed Fitouhi (1)

1 Analyse harmonique et fonctions spéciales

In this paper we study the positivity of the generalized $q$-translation associated with the $q$-Bessel Hahn Exton function which is deduced by a new formulation of the Graf's addition formula related to this function.

Mots clés: Graf's addition theorem; q-Bessel function; $q$-Bessel translation operator

Domaines: Analyse classique [math.CA]; Mathématiques générales [math.GM]

Lazhar Dhaouadi, Ahmed Fitouhi. On the Graf's addition theorem for Hahn Exton q-Bessel function. Constructive Approximation, 2011, 34, pp.453-472. ⟨10.1007/s00365-011-9132-0⟩. ⟨hal-00161528v2⟩