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

Lazhar Dhaouadi (1)

1 Analyse harmonique et fonctions spéciales

It is the purpose of this note to give a new interpretation of the Graf's addition formula for Hahn Exton q-Bessel function using the properties of the $q$-Bessel Fourier transform. In the rest of this note we establish a connection between this result and the positivity of the $q$-Bessel translation operator.

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

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

Lazhar Dhaouadi. On the Graf's addition theorem for Hahn Exton q-Bessel function. 2007. ⟨hal-00161528v1⟩