Efficient Multi-Precision Computation of Bessel Functions for Real Orders and Complex Arguments with Fortran Implementation -- Part II: The Modified Bessel Func... (opens in new tab)

This paper, the second in a series, presents an efficient, self-contained algorithm for computing the modified Bessel function of the second kind, \(K_{\nu}(z)\) for complex argument and real orders, building on Part~I (for \(I_{\nu}\)). The method adaptively selects among analytic representations such as power series, large-\(|z|\) asymptotics, uniform asymptotics for large \(|\nu|\), and numerically stable forward recurrence with region bounda...