Canonical Scattering Coefficients Upward Recursion Algorithm for Multilayered Sphere or Long Cylinder with Large Size Parameters

Calculation of the scattering coefficients appearing in Mie theory involves recursive relations for Bessel or Riccati-Bessel functions. Canonical recommendations prescribe using both upward and downward recursions for different types of functions. This makes the computational algorithm rather cumbersome. We have justified here the procedure using the upward recursions only, whose results are as stable as the canonical recommendations.Calculation of the scattering coefficients appearing in Mie theory involves recursive relations for Bessel or Riccati-Bessel functions. Canonical recommendations prescribe using both upward and downward recursions for different types of functions. This makes the computational algorithm rather cumbersome. We have justified here the procedure using the upward recursions only, whose results are as stable as the canonical recommendations.