Calculation of auxiliary functions related to Riccati Bessel functions in Mie scattering
Abstract In Mie scattering calculation, auxiliary functions, such as the logarithmic derivatives, the ratios and the products of Riccati Bessel functions, are used to recast the formulae of the scattering coefficients so as to circumvent the difficulty. So far, there are still problems left unsolved. The paper presents the recursive algorithms for the calculation of these functions. The logarithmic derivatives and are calculated firstly, and then, they are used for the calculation of the ratio These three functions can be further used to calculate the other auxiliary functions and also the Riccati Bessel function themselves. Numerical results show that the algorithm is stable and reliable except for some special cases.