On some relations between hyper Bessel–Clifford, Macdonald and Meijer functions and hyper Hankel–Clifford integral transforms

Abstract

Using a representation of the unimodular Lorentz group, we derive some relations between hyper Bessel–Clifford, Macdonald and Meijer functions. We obtained them as two additional theorems (continual and countable) for a functional defined on the above group and a pair of basis functions belonging to representation spaces. Introducing a hyper analogue of the known first and second Hankel–Clifford integral transforms and writing the continual addition theorem for a particular case, we obtain a simple formula for the sum of these transforms of Macdonald function.