We prove a limit relation for the Dunkl–Bessel function of type BN with multiplicity parameters k1 on the roots ±ei and k2 on ±ei ± ej where k1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkltype Bessel function of type AN−1 with multiplicity k2. For certain values of k2 an improved estimate is obtained from a corresponding limit rela...

A previous fully relativistic time-dependent close-coupling method [Phys. Rev. A 81, 063431 (2010)], developed to study the photoionization of highly charged atomic ions, is substantially modified to include the full electromagnetic-field potential. Expansion of a one active electron wave function for the time-dependent Dirac equation in spin-orbit eigenfunctions yields close-coupled equations ...

We show that in addition to well-known Bessel, Hermite–Gauss and Laguerre– Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of ρ. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, ...

In this paper some Turán type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Turánian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions.