Evaluation of Hankel functions with complex argument and complex order

The use of F.W.J. Olver's (1974) uniform asymptotic expansions to compute Hankel functions (of interest in EM scattering) of complex argument z and complex order v is examined. Emphasis is placed on how to choose the proper branches in evaluation of the complex functions in the asymptotic representations. Comparison is made with the nonuniform formulas of Debye and Watson. The Debye formulas are valid when z and v are far apart, and the Watson formulas are valid when z and v are close together. The fact that the Olver formulas are uniform is important from a numerical viewpoint, because a satisfactory criterion for deciding when to switch between the Debye and Watson (1958) formulas is not available. Validation by comparison with two nonasymptotic methods verifies that the Olver formulas are considerably more accurate than the Debye or Watson formulas.<
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