Analytic partial wave expansion and integral representation of Bessel beam

This paper describes the partial wave expansion and integral representation of Bessel beams in free space and in the presence of dispersion. The expansion of the Bessel beam wavepacket with constant spectrum is obtained as well. Furthermore, the sum of a triple Legendre polynomial product of same order but different argument follows naturally from the partial wave expansion. The integration of all Bessel beams over all conical angles is shown to have a simple series representation, which confirms the equivalence between the results for both expansion and integral representation.