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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.
Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric functi
In this note, we derive the closed-form expression for the summation of series $sum_{n=0}^{infty}nJ_n(x)partial J_n/partial n$, which is found in the calculation of entanglement entropy in 2-d bosonic free field, in terms of $Y_0$, $J_0$ and an integ
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
We present a summary of recent and older results on Bessel integrals and their relation with zeta numbers.
The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater spinor orbital