In the design of linear arrays containing an odd number of elements with constant element spacing of less than a half wavelength, the mathematical problem reduces to that of finding explicitly the coefficients, b_m, in the expansion where a and b are constants, n > 0, and T_m(x) is defined as cos (m arc cos x) for m ≥ 0. Such a problem was initially solved by DuHamel and later given by Salzer in a form more convenient for computation. The purpose of this paper is to give an alternative derivation of Salzer's result, making use of the orthogonality properties the Chebyshev polynomials in order to obviate the fairly elaborate series manipulations required in the previous derivation.