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Most "traditional" Mie calculations algorithms make use of the An function, i.e. the logarithmic derivative of the Ricatti-Bessel function, which is calculated through recurrence relationships or the continued-fraction algorithm. From that perspective it is interesting to note that numerators and denominators of functions an and bn satisfy recurrence relationships (Verner B 1976). Bohren CF 1987b showed that the functions themselves also satisfy recurrence relationships, and consequently can be calculated on their own, in principle, from the values of the four first functions a1, a2, b1, and b2.
Some algorithms (for example, Du H 2004, Cachorro VE and Salcedo 1991) do away with the logarithmic derivative of the Ricatti-Bessel function, i.e. the An function, and reformulate the an and bn functions by using ratios of the successive orders of the Ricatti-Bessel functions instead.
| CITATION: Jonasz M. 2006. Mie theory: Other algorithms for functions a and b (www.tpdsci.com/Tpc/MieCalcAwAlt.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 18-Apr-2006 Modified: 19-Jun-2006 Peer-reviewed: PENDING |
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