Evaluation of the Modified Bessel Function of the Third Kind of Imaginary Orders

Abstract

C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Modelling, Analysis and Simulation

Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments

“…As discussed in [7] both K ia (x) and K ia can be computed for moderate a by means of a continued fraction method, similar to the corresponding method for Bessel functions of real orders (see [16] and [12], pp. 239-240).…”

“…The coefficients f k and r k differ from those in [7] by a constant factor (for fixed a). The new normalization shows explicitly (Eqs.…”

“…Indeed, as it was discussed in [7], the steepest descent method leads to three integrals, which have to be computed separately. However, as we later discuss, for moderately large a it will be enough to compute a single integral.…”

“…The function K ia (x) finds application in a number of problems of physics and applied mathematics [7]. The function L ia (x) is a real valued numerically satisfactory companion to K ia (x) in the sense described in [11], pp.…”

“…We avoid duplicating information already given in previous papers; in particular, the references [7; 8] provide information required for building the algorithms of the accompanying paper [6]. A few misprints in [7] are corrected.…”