Figure 10.

A scheme for stable recursive computation of the rotation coefficients. On the left, the process of recursive computation of the values of the coefficient for different values of m, m′ (displayed on a grid) is shown. The ● values are computed from the main diagonal for which the values are directly obtained. These are indicated by ○. To compute values at all nodes in the shaded area one needs the values on the subdiagonal (the dashed line). These values are obtained via the flip transform from the rotation coefficients for β = π/2, which are computed recursively via the process shown on the right. Initial values at the nodes marked by ○ are computed using analytical formulae. The values of the rotation coefficients in the entire domain m′, m = −n, …, n can be obtained from the values in the shaded domains using symmetry relations.