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Bessel function expansions of Coulomb wave functions. (English) Zbl 0605.33004
From the convergence properties of the expansion of the function Φ r --1 F in powers of the energy, we successively obtain the expansions of F and G as single series of modified Bessel functions I 2+1+n and K 2+1+n , respectively, as well as corresponding asymptotic approximations of G for |η|. Both repulsive and attractive fields are considered for real and complex energies as well. The expansion of F is not new, but its convergence is given a simpler and corrected proof. The simplest form of the asymptotic approximations obtained for G , in the case of a repulsive field and for low positive energies, is compared to an expansion obtained by Abramowitz.
33C10Bessel and Airy functions, cylinder functions, 0 F 1
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)