Calculating Fourier coefficients for Chebyshev patterns by recurrence formulas

Two recurrence schemes are given for finding A
m
in T
n
(ax + b) = Σ
m=0
ⁿ
A
m
T
m
(x) for given n, a, and b, where T
m
(x)= cos (m arccos x). This problem arises in the calculation of feeding coefficients to produce optimum beam patterns in the design of certain linear arrays.