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Coulomb and Bessel functions of complex arguments and order. (English) Zbl 0626.65014
The differential equation f '' (ρ)+(1-2η/ρ-λ(λ+1)/ρ 2 )f(ρ)=0 has two linearly independent solutions F λ (η,ρ) and G λ (η,ρ) called Coulomb wavefunctions. The real functions F λ , G λ , (d/dρ)G λ and (d/dρ)F λ have been studied extensively and methods of calculations have been developed by several authors. The most important technique has been developed by the second author et al. in 1974, where the authors calculate regular and irregular functions and their derivatives for any real λ or for a range of integer-spaced λ-values. In the present paper the authors define Columb wavefunctions in the complex case and generalize the earlier method to calculate the functions F λ , G λ , (d/dρ)F λ and (d/dρ)G λ where all variables are complex.
Reviewer: A.Laforgia
MSC:
65D20Computation of special functions, construction of tables
65E05Numerical methods in complex analysis
33E15Other wave functions
33C10Bessel and Airy functions, cylinder functions, 0 F 1