Table 2.

Coefficient conversion relationships for different values of m and K where N = m + 2K = 7

m	K	New expansion coefficients bn,m
5	1	$\begin{array}{l}{b}_{7,5}=\frac{1}{{\lambda }^7}{a}_{7,5}\\ b_{5,5}=\frac{1}{{\lambda }^5}\left[a_{5,5}-4\sqrt{3}\left(1-\frac{1}{{\lambda }^2}\right)a_{7,5}\right]\end{array}$
3	2	$\begin{array}{l}{b}_{7,3}=\frac{1}{{\lambda }^7}{a}_{7,3}\\ b_{5,3}=\frac{1}{{\lambda }^5}\left[a_{5,3}-4\sqrt{3}\left(1-\frac{1}{{\lambda }^2}\right)a_{7,3}\right]\\ b_{3,3}=\frac{1}{{\lambda }^3}\left[a_{3,3}-2\sqrt{6}\left(1-\frac{1}{{\lambda }^2}\right)a_{5,3}+2\sqrt{2}\left(5-\frac{12}{{\lambda }^2}+\frac{7}{{\lambda }^4}\right)a_{7,3}\right]\end{array}$
1	3	$\begin{array}{l}{b}_{7,1}=\frac{1}{{\lambda }^7}{a}_{7,1}\\ b_{5,1}=\frac{1}{{\lambda }^5}\left[a_{5,1}-4\sqrt{3}\left(1-\frac{1}{{\lambda }^2}\right)a_{7,1}\right]\\ b_{3,1}=\frac{1}{{\lambda }^3}\left[a_{3,1}-2\sqrt{6}\left(1-\frac{1}{{\lambda }^2}\right)a_{5,1}+2\sqrt{2}\left(5-\frac{12}{{\lambda }^2}+\frac{7}{{\lambda }^4}\right)a_{7,1}\right]\\ b_{1,1}=\frac{1}{\lambda }\left[a_{1,1}-2\sqrt{2}\left(1-\frac{1}{{\lambda }^2}\right)a_{3,1}+\sqrt{3}\left(3-\frac{8}{{\lambda }^2}+\frac{5}{{\lambda }^4}\right)a_{5,1}-4\left(2-\frac{10}{{\lambda }^2}+\frac{15}{{\lambda }^4}-\frac{7}{{\lambda }^6}\right)a_{7,1}\right]\end{array}$